--- _id: '16513' author: - first_name: P. J. full_name: Aston, P. J. last_name: Aston - first_name: M. full_name: Dellnitz, M. last_name: Dellnitz citation: ama: 'Aston PJ, Dellnitz M. The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms. In: Equadiff 99. ; 2000. doi:10.1142/9789812792617_0196' apa: Aston, P. J., & Dellnitz, M. (2000). The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms. In Equadiff 99. https://doi.org/10.1142/9789812792617_0196 bibtex: '@inbook{Aston_Dellnitz_2000, title={The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms}, DOI={10.1142/9789812792617_0196}, booktitle={Equadiff 99}, author={Aston, P. J. and Dellnitz, M.}, year={2000} }' chicago: Aston, P. J., and M. Dellnitz. “The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms.” In Equadiff 99, 2000. https://doi.org/10.1142/9789812792617_0196. ieee: P. J. Aston and M. Dellnitz, “The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms,” in Equadiff 99, 2000. mla: Aston, P. J., and M. Dellnitz. “The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms.” Equadiff 99, 2000, doi:10.1142/9789812792617_0196. short: 'P.J. Aston, M. Dellnitz, in: Equadiff 99, 2000.' date_created: 2020-04-15T07:53:09Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1142/9789812792617_0196 language: - iso: eng publication: Equadiff 99 publication_identifier: isbn: - '9789810243593' - '9789812792617' publication_status: published status: public title: The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms type: book_chapter user_id: '15701' year: '2000' ... --- _id: '16553' author: - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Gary full_name: Froyland, Gary last_name: Froyland - first_name: Stefan full_name: Sertl, Stefan last_name: Sertl citation: ama: 'Dellnitz M, Froyland G, Sertl S. A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator. In: Equadiff 99. ; 2000. doi:10.1142/9789812792617_0199' apa: Dellnitz, M., Froyland, G., & Sertl, S. (2000). A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator. In Equadiff 99. https://doi.org/10.1142/9789812792617_0199 bibtex: '@inbook{Dellnitz_Froyland_Sertl_2000, title={A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator}, DOI={10.1142/9789812792617_0199}, booktitle={Equadiff 99}, author={Dellnitz, Michael and Froyland, Gary and Sertl, Stefan}, year={2000} }' chicago: Dellnitz, Michael, Gary Froyland, and Stefan Sertl. “A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator.” In Equadiff 99, 2000. https://doi.org/10.1142/9789812792617_0199. ieee: M. Dellnitz, G. Froyland, and S. Sertl, “A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator,” in Equadiff 99, 2000. mla: Dellnitz, Michael, et al. “A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator.” Equadiff 99, 2000, doi:10.1142/9789812792617_0199. short: 'M. Dellnitz, G. Froyland, S. Sertl, in: Equadiff 99, 2000.' date_created: 2020-04-15T09:08:34Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1142/9789812792617_0199 language: - iso: eng publication: Equadiff 99 publication_identifier: isbn: - '9789810243593' - '9789812792617' publication_status: published status: public title: A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator type: book_chapter user_id: '15701' year: '2000' ... --- _id: '16554' author: - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Gary full_name: Froyland, Gary last_name: Froyland - first_name: Stefan full_name: Sertl, Stefan last_name: Sertl citation: ama: Dellnitz M, Froyland G, Sertl S. On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity. 2000:1171-1188. doi:10.1088/0951-7715/13/4/310 apa: Dellnitz, M., Froyland, G., & Sertl, S. (2000). On the isolated spectrum of the Perron-Frobenius operator. Nonlinearity, 1171–1188. https://doi.org/10.1088/0951-7715/13/4/310 bibtex: '@article{Dellnitz_Froyland_Sertl_2000, title={On the isolated spectrum of the Perron-Frobenius operator}, DOI={10.1088/0951-7715/13/4/310}, journal={Nonlinearity}, author={Dellnitz, Michael and Froyland, Gary and Sertl, Stefan}, year={2000}, pages={1171–1188} }' chicago: Dellnitz, Michael, Gary Froyland, and Stefan Sertl. “On the Isolated Spectrum of the Perron-Frobenius Operator.” Nonlinearity, 2000, 1171–88. https://doi.org/10.1088/0951-7715/13/4/310. ieee: M. Dellnitz, G. Froyland, and S. Sertl, “On the isolated spectrum of the Perron-Frobenius operator,” Nonlinearity, pp. 1171–1188, 2000. mla: Dellnitz, Michael, et al. “On the Isolated Spectrum of the Perron-Frobenius Operator.” Nonlinearity, 2000, pp. 1171–88, doi:10.1088/0951-7715/13/4/310. short: M. Dellnitz, G. Froyland, S. Sertl, Nonlinearity (2000) 1171–1188. date_created: 2020-04-15T09:09:46Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1088/0951-7715/13/4/310 language: - iso: eng page: 1171-1188 publication: Nonlinearity publication_identifier: issn: - 0951-7715 - 1361-6544 publication_status: published status: public title: On the isolated spectrum of the Perron-Frobenius operator type: journal_article user_id: '15701' year: '2000' ... --- _id: '16616' author: - first_name: Oliver full_name: Junge, Oliver last_name: Junge citation: ama: 'Junge O. Rigorous discretization of subdivision techniques. In: Equadiff 99. ; 2000. doi:10.1142/9789812792617_0178' apa: Junge, O. (2000). Rigorous discretization of subdivision techniques. In Equadiff 99. https://doi.org/10.1142/9789812792617_0178 bibtex: '@inbook{Junge_2000, title={Rigorous discretization of subdivision techniques}, DOI={10.1142/9789812792617_0178}, booktitle={Equadiff 99}, author={Junge, Oliver}, year={2000} }' chicago: Junge, Oliver. “Rigorous Discretization of Subdivision Techniques.” In Equadiff 99, 2000. https://doi.org/10.1142/9789812792617_0178. ieee: O. Junge, “Rigorous discretization of subdivision techniques,” in Equadiff 99, 2000. mla: Junge, Oliver. “Rigorous Discretization of Subdivision Techniques.” Equadiff 99, 2000, doi:10.1142/9789812792617_0178. short: 'O. Junge, in: Equadiff 99, 2000.' date_created: 2020-04-16T08:07:52Z date_updated: 2022-01-06T06:52:53Z department: - _id: '101' doi: 10.1142/9789812792617_0178 language: - iso: eng publication: Equadiff 99 publication_identifier: isbn: - '9789810243593' - '9789812792617' publication_status: published status: public title: Rigorous discretization of subdivision techniques type: book_chapter user_id: '15701' year: '2000' ... --- _id: '17018' author: - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Oliver full_name: Junge, Oliver last_name: Junge - first_name: Martin full_name: Rumpf, Martin last_name: Rumpf - first_name: Robert full_name: Strzodka, Robert last_name: Strzodka citation: ama: 'Dellnitz M, Junge O, Rumpf M, Strzodka R. The computation of an unstable invariant set inside a cylinder containing a knotted flow. In: Equadiff 99. ; 2000:1053--1059. doi:10.1142/9789812792617_0204' apa: Dellnitz, M., Junge, O., Rumpf, M., & Strzodka, R. (2000). The computation of an unstable invariant set inside a cylinder containing a knotted flow. In Equadiff 99 (pp. 1053--1059). https://doi.org/10.1142/9789812792617_0204 bibtex: '@inbook{Dellnitz_Junge_Rumpf_Strzodka_2000, title={The computation of an unstable invariant set inside a cylinder containing a knotted flow}, DOI={10.1142/9789812792617_0204}, booktitle={Equadiff 99}, author={Dellnitz, Michael and Junge, Oliver and Rumpf, Martin and Strzodka, Robert}, year={2000}, pages={1053--1059} }' chicago: Dellnitz, Michael, Oliver Junge, Martin Rumpf, and Robert Strzodka. “The Computation of an Unstable Invariant Set inside a Cylinder Containing a Knotted Flow.” In Equadiff 99, 1053--1059, 2000. https://doi.org/10.1142/9789812792617_0204. ieee: M. Dellnitz, O. Junge, M. Rumpf, and R. Strzodka, “The computation of an unstable invariant set inside a cylinder containing a knotted flow,” in Equadiff 99, 2000, pp. 1053--1059. mla: Dellnitz, Michael, et al. “The Computation of an Unstable Invariant Set inside a Cylinder Containing a Knotted Flow.” Equadiff 99, 2000, pp. 1053--1059, doi:10.1142/9789812792617_0204. short: 'M. Dellnitz, O. Junge, M. Rumpf, R. Strzodka, in: Equadiff 99, 2000, pp. 1053--1059.' date_created: 2020-05-19T09:13:56Z date_updated: 2022-01-06T06:53:02Z department: - _id: '101' doi: 10.1142/9789812792617_0204 language: - iso: eng page: 1053--1059 publication: Equadiff 99 publication_identifier: isbn: - '9789810243593' - '9789812792617' publication_status: published status: public title: The computation of an unstable invariant set inside a cylinder containing a knotted flow type: book_chapter user_id: '32643' year: '2000' ... --- _id: '16511' author: - first_name: Philip J. full_name: Aston, Philip J. last_name: Aston - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz citation: ama: Aston PJ, Dellnitz M. The computation of lyapunov exponents via spatial integration with application to blowout bifurcations. Computer Methods in Applied Mechanics and Engineering. 1999:223-237. doi:10.1016/s0045-7825(98)00196-0 apa: Aston, P. J., & Dellnitz, M. (1999). The computation of lyapunov exponents via spatial integration with application to blowout bifurcations. Computer Methods in Applied Mechanics and Engineering, 223–237. https://doi.org/10.1016/s0045-7825(98)00196-0 bibtex: '@article{Aston_Dellnitz_1999, title={The computation of lyapunov exponents via spatial integration with application to blowout bifurcations}, DOI={10.1016/s0045-7825(98)00196-0}, journal={Computer Methods in Applied Mechanics and Engineering}, author={Aston, Philip J. and Dellnitz, Michael}, year={1999}, pages={223–237} }' chicago: Aston, Philip J., and Michael Dellnitz. “The Computation of Lyapunov Exponents via Spatial Integration with Application to Blowout Bifurcations.” Computer Methods in Applied Mechanics and Engineering, 1999, 223–37. https://doi.org/10.1016/s0045-7825(98)00196-0. ieee: P. J. Aston and M. Dellnitz, “The computation of lyapunov exponents via spatial integration with application to blowout bifurcations,” Computer Methods in Applied Mechanics and Engineering, pp. 223–237, 1999. mla: Aston, Philip J., and Michael Dellnitz. “The Computation of Lyapunov Exponents via Spatial Integration with Application to Blowout Bifurcations.” Computer Methods in Applied Mechanics and Engineering, 1999, pp. 223–37, doi:10.1016/s0045-7825(98)00196-0. short: P.J. Aston, M. Dellnitz, Computer Methods in Applied Mechanics and Engineering (1999) 223–237. date_created: 2020-04-15T07:27:08Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1016/s0045-7825(98)00196-0 language: - iso: eng page: 223-237 publication: Computer Methods in Applied Mechanics and Engineering publication_identifier: issn: - 0045-7825 publication_status: published status: public title: The computation of lyapunov exponents via spatial integration with application to blowout bifurcations type: journal_article user_id: '15701' year: '1999' ... --- _id: '16537' author: - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Oliver full_name: Junge, Oliver last_name: Junge citation: ama: Dellnitz M, Junge O. On the Approximation of Complicated Dynamical Behavior. SIAM Journal on Numerical Analysis. 1999:491-515. doi:10.1137/s0036142996313002 apa: Dellnitz, M., & Junge, O. (1999). On the Approximation of Complicated Dynamical Behavior. SIAM Journal on Numerical Analysis, 491–515. https://doi.org/10.1137/s0036142996313002 bibtex: '@article{Dellnitz_Junge_1999, title={On the Approximation of Complicated Dynamical Behavior}, DOI={10.1137/s0036142996313002}, journal={SIAM Journal on Numerical Analysis}, author={Dellnitz, Michael and Junge, Oliver}, year={1999}, pages={491–515} }' chicago: Dellnitz, Michael, and Oliver Junge. “On the Approximation of Complicated Dynamical Behavior.” SIAM Journal on Numerical Analysis, 1999, 491–515. https://doi.org/10.1137/s0036142996313002. ieee: M. Dellnitz and O. Junge, “On the Approximation of Complicated Dynamical Behavior,” SIAM Journal on Numerical Analysis, pp. 491–515, 1999. mla: Dellnitz, Michael, and Oliver Junge. “On the Approximation of Complicated Dynamical Behavior.” SIAM Journal on Numerical Analysis, 1999, pp. 491–515, doi:10.1137/s0036142996313002. short: M. Dellnitz, O. Junge, SIAM Journal on Numerical Analysis (1999) 491–515. date_created: 2020-04-15T08:35:45Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1137/s0036142996313002 language: - iso: eng page: 491-515 publication: SIAM Journal on Numerical Analysis publication_identifier: issn: - 0036-1429 - 1095-7170 publication_status: published status: public title: On the Approximation of Complicated Dynamical Behavior type: journal_article user_id: '15701' year: '1999' ... --- _id: '16584' author: - first_name: Peter full_name: Deuflhard, Peter last_name: Deuflhard - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Oliver full_name: Junge, Oliver last_name: Junge - first_name: Christof full_name: Schütte, Christof last_name: Schütte citation: ama: 'Deuflhard P, Dellnitz M, Junge O, Schütte C. Computation of Essential Molecular Dynamics by Subdivision Techniques. In: Computational Molecular Dynamics: Challenges, Methods, Ideas. Berlin, Heidelberg; 1999. doi:10.1007/978-3-642-58360-5_5' apa: 'Deuflhard, P., Dellnitz, M., Junge, O., & Schütte, C. (1999). Computation of Essential Molecular Dynamics by Subdivision Techniques. In Computational Molecular Dynamics: Challenges, Methods, Ideas. Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58360-5_5' bibtex: '@inbook{Deuflhard_Dellnitz_Junge_Schütte_1999, place={Berlin, Heidelberg}, title={Computation of Essential Molecular Dynamics by Subdivision Techniques}, DOI={10.1007/978-3-642-58360-5_5}, booktitle={Computational Molecular Dynamics: Challenges, Methods, Ideas}, author={Deuflhard, Peter and Dellnitz, Michael and Junge, Oliver and Schütte, Christof}, year={1999} }' chicago: 'Deuflhard, Peter, Michael Dellnitz, Oliver Junge, and Christof Schütte. “Computation of Essential Molecular Dynamics by Subdivision Techniques.” In Computational Molecular Dynamics: Challenges, Methods, Ideas. Berlin, Heidelberg, 1999. https://doi.org/10.1007/978-3-642-58360-5_5.' ieee: 'P. Deuflhard, M. Dellnitz, O. Junge, and C. Schütte, “Computation of Essential Molecular Dynamics by Subdivision Techniques,” in Computational Molecular Dynamics: Challenges, Methods, Ideas, Berlin, Heidelberg, 1999.' mla: 'Deuflhard, Peter, et al. “Computation of Essential Molecular Dynamics by Subdivision Techniques.” Computational Molecular Dynamics: Challenges, Methods, Ideas, 1999, doi:10.1007/978-3-642-58360-5_5.' short: 'P. Deuflhard, M. Dellnitz, O. Junge, C. Schütte, in: Computational Molecular Dynamics: Challenges, Methods, Ideas, Berlin, Heidelberg, 1999.' date_created: 2020-04-16T05:43:16Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1007/978-3-642-58360-5_5 language: - iso: eng place: Berlin, Heidelberg publication: 'Computational Molecular Dynamics: Challenges, Methods, Ideas' publication_identifier: isbn: - '9783540632429' - '9783642583605' issn: - 1439-7358 publication_status: published status: public title: Computation of Essential Molecular Dynamics by Subdivision Techniques type: book_chapter user_id: '15701' year: '1999' ... --- _id: '17017' author: - first_name: David full_name: Bürkle, David last_name: Bürkle - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Oliver full_name: Junge, Oliver last_name: Junge - first_name: Martin full_name: Rumpf, Martin last_name: Rumpf - first_name: Michael full_name: Spielberg, Michael last_name: Spielberg citation: ama: Bürkle D, Dellnitz M, Junge O, Rumpf M, Spielberg M. Visualizing Complicated Dynamics. Proceedings of Visualization 99. 1999. apa: Bürkle, D., Dellnitz, M., Junge, O., Rumpf, M., & Spielberg, M. (1999). Visualizing Complicated Dynamics. Proceedings of Visualization 99. bibtex: '@article{Bürkle_Dellnitz_Junge_Rumpf_Spielberg_1999, title={Visualizing Complicated Dynamics}, journal={Proceedings of Visualization 99}, author={Bürkle, David and Dellnitz, Michael and Junge, Oliver and Rumpf, Martin and Spielberg, Michael}, year={1999} }' chicago: Bürkle, David, Michael Dellnitz, Oliver Junge, Martin Rumpf, and Michael Spielberg. “Visualizing Complicated Dynamics.” Proceedings of Visualization 99, 1999. ieee: D. Bürkle, M. Dellnitz, O. Junge, M. Rumpf, and M. Spielberg, “Visualizing Complicated Dynamics,” Proceedings of Visualization 99, 1999. mla: Bürkle, David, et al. “Visualizing Complicated Dynamics.” Proceedings of Visualization 99, 1999. short: D. Bürkle, M. Dellnitz, O. Junge, M. Rumpf, M. Spielberg, Proceedings of Visualization 99 (1999). date_created: 2020-05-19T09:12:53Z date_updated: 2022-01-06T06:53:02Z department: - _id: '101' language: - iso: eng publication: Proceedings of Visualization 99 status: public title: Visualizing Complicated Dynamics type: journal_article user_id: '32643' year: '1999' ... --- _id: '16536' author: - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Oliver full_name: Junge, Oliver last_name: Junge citation: ama: Dellnitz M, Junge O. An adaptive subdivision technique for the approximation of attractors and invariant measures. Computing and Visualization in Science. 1998:63-68. doi:10.1007/s007910050006 apa: Dellnitz, M., & Junge, O. (1998). An adaptive subdivision technique for the approximation of attractors and invariant measures. Computing and Visualization in Science, 63–68. https://doi.org/10.1007/s007910050006 bibtex: '@article{Dellnitz_Junge_1998, title={An adaptive subdivision technique for the approximation of attractors and invariant measures}, DOI={10.1007/s007910050006}, journal={Computing and Visualization in Science}, author={Dellnitz, Michael and Junge, Oliver}, year={1998}, pages={63–68} }' chicago: Dellnitz, Michael, and Oliver Junge. “An Adaptive Subdivision Technique for the Approximation of Attractors and Invariant Measures.” Computing and Visualization in Science, 1998, 63–68. https://doi.org/10.1007/s007910050006. ieee: M. Dellnitz and O. Junge, “An adaptive subdivision technique for the approximation of attractors and invariant measures,” Computing and Visualization in Science, pp. 63–68, 1998. mla: Dellnitz, Michael, and Oliver Junge. “An Adaptive Subdivision Technique for the Approximation of Attractors and Invariant Measures.” Computing and Visualization in Science, 1998, pp. 63–68, doi:10.1007/s007910050006. short: M. Dellnitz, O. Junge, Computing and Visualization in Science (1998) 63–68. date_created: 2020-04-15T08:33:03Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1007/s007910050006 language: - iso: eng page: 63-68 publication: Computing and Visualization in Science publication_identifier: issn: - 1432-9360 - 1433-0369 publication_status: published status: public title: An adaptive subdivision technique for the approximation of attractors and invariant measures type: journal_article user_id: '15701' year: '1998' ... --- _id: '16535' abstract: - lang: eng text: Recently multilevel subdivision techniques have been introduced in the numerical investigation of complicated dynamical behavior. We illustrate the applicability and efficiency of these methods by a detailed numerical study of Chua's circuit. In particular we will show that there exist two regions in phase space which are almost invariant in the sense that typical trajectories stay inside each of these sets on average for quite a long time. author: - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Oliver full_name: Junge, Oliver last_name: Junge citation: ama: Dellnitz M, Junge O. Almost Invariant Sets in Chua’s Circuit. International Journal of Bifurcation and Chaos. 1997:2475-2485. doi:10.1142/s0218127497001655 apa: Dellnitz, M., & Junge, O. (1997). Almost Invariant Sets in Chua’s Circuit. International Journal of Bifurcation and Chaos, 2475–2485. https://doi.org/10.1142/s0218127497001655 bibtex: '@article{Dellnitz_Junge_1997, title={Almost Invariant Sets in Chua’s Circuit}, DOI={10.1142/s0218127497001655}, journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael and Junge, Oliver}, year={1997}, pages={2475–2485} }' chicago: Dellnitz, Michael, and Oliver Junge. “Almost Invariant Sets in Chua’s Circuit.” International Journal of Bifurcation and Chaos, 1997, 2475–85. https://doi.org/10.1142/s0218127497001655. ieee: M. Dellnitz and O. Junge, “Almost Invariant Sets in Chua’s Circuit,” International Journal of Bifurcation and Chaos, pp. 2475–2485, 1997. mla: Dellnitz, Michael, and Oliver Junge. “Almost Invariant Sets in Chua’s Circuit.” International Journal of Bifurcation and Chaos, 1997, pp. 2475–85, doi:10.1142/s0218127497001655. short: M. Dellnitz, O. Junge, International Journal of Bifurcation and Chaos (1997) 2475–2485. date_created: 2020-04-15T08:31:50Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1142/s0218127497001655 language: - iso: eng page: 2475-2485 publication: International Journal of Bifurcation and Chaos publication_identifier: issn: - 0218-1274 - 1793-6551 publication_status: published status: public title: Almost Invariant Sets in Chua's Circuit type: journal_article user_id: '15701' year: '1997' ... --- _id: '16552' author: - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Andreas full_name: Hohmann, Andreas last_name: Hohmann - first_name: Oliver full_name: Junge, Oliver last_name: Junge - first_name: Martin full_name: Rumpf, Martin last_name: Rumpf citation: ama: 'Dellnitz M, Hohmann A, Junge O, Rumpf M. Exploring invariant sets and invariant measures. Chaos: An Interdisciplinary Journal of Nonlinear Science. 1997:221-228. doi:10.1063/1.166223' apa: 'Dellnitz, M., Hohmann, A., Junge, O., & Rumpf, M. (1997). Exploring invariant sets and invariant measures. Chaos: An Interdisciplinary Journal of Nonlinear Science, 221–228. https://doi.org/10.1063/1.166223' bibtex: '@article{Dellnitz_Hohmann_Junge_Rumpf_1997, title={Exploring invariant sets and invariant measures}, DOI={10.1063/1.166223}, journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, author={Dellnitz, Michael and Hohmann, Andreas and Junge, Oliver and Rumpf, Martin}, year={1997}, pages={221–228} }' chicago: 'Dellnitz, Michael, Andreas Hohmann, Oliver Junge, and Martin Rumpf. “Exploring Invariant Sets and Invariant Measures.” Chaos: An Interdisciplinary Journal of Nonlinear Science, 1997, 221–28. https://doi.org/10.1063/1.166223.' ieee: 'M. Dellnitz, A. Hohmann, O. Junge, and M. Rumpf, “Exploring invariant sets and invariant measures,” Chaos: An Interdisciplinary Journal of Nonlinear Science, pp. 221–228, 1997.' mla: 'Dellnitz, Michael, et al. “Exploring Invariant Sets and Invariant Measures.” Chaos: An Interdisciplinary Journal of Nonlinear Science, 1997, pp. 221–28, doi:10.1063/1.166223.' short: 'M. Dellnitz, A. Hohmann, O. Junge, M. Rumpf, Chaos: An Interdisciplinary Journal of Nonlinear Science (1997) 221–228.' date_created: 2020-04-15T09:06:28Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1063/1.166223 language: - iso: eng page: 221-228 publication: 'Chaos: An Interdisciplinary Journal of Nonlinear Science' publication_identifier: issn: - 1054-1500 - 1089-7682 publication_status: published status: public title: Exploring invariant sets and invariant measures type: journal_article user_id: '15701' year: '1997' ... --- _id: '16614' author: - first_name: Rabbijah full_name: Guder, Rabbijah last_name: Guder - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Edwin full_name: Kreuzer, Edwin last_name: Kreuzer citation: ama: Guder R, Dellnitz M, Kreuzer E. An adaptive method for the approximation of the generalized cell mapping. Chaos, Solitons & Fractals. 1997:525-534. doi:10.1016/s0960-0779(96)00118-x apa: Guder, R., Dellnitz, M., & Kreuzer, E. (1997). An adaptive method for the approximation of the generalized cell mapping. Chaos, Solitons & Fractals, 525–534. https://doi.org/10.1016/s0960-0779(96)00118-x bibtex: '@article{Guder_Dellnitz_Kreuzer_1997, title={An adaptive method for the approximation of the generalized cell mapping}, DOI={10.1016/s0960-0779(96)00118-x}, journal={Chaos, Solitons & Fractals}, author={Guder, Rabbijah and Dellnitz, Michael and Kreuzer, Edwin}, year={1997}, pages={525–534} }' chicago: Guder, Rabbijah, Michael Dellnitz, and Edwin Kreuzer. “An Adaptive Method for the Approximation of the Generalized Cell Mapping.” Chaos, Solitons & Fractals, 1997, 525–34. https://doi.org/10.1016/s0960-0779(96)00118-x. ieee: R. Guder, M. Dellnitz, and E. Kreuzer, “An adaptive method for the approximation of the generalized cell mapping,” Chaos, Solitons & Fractals, pp. 525–534, 1997. mla: Guder, Rabbijah, et al. “An Adaptive Method for the Approximation of the Generalized Cell Mapping.” Chaos, Solitons & Fractals, 1997, pp. 525–34, doi:10.1016/s0960-0779(96)00118-x. short: R. Guder, M. Dellnitz, E. Kreuzer, Chaos, Solitons & Fractals (1997) 525–534. date_created: 2020-04-16T08:05:37Z date_updated: 2022-01-06T06:52:53Z department: - _id: '101' doi: 10.1016/s0960-0779(96)00118-x language: - iso: eng page: 525-534 publication: Chaos, Solitons & Fractals publication_identifier: issn: - 0960-0779 publication_status: published status: public title: An adaptive method for the approximation of the generalized cell mapping type: journal_article user_id: '15701' year: '1997' ... --- _id: '17015' author: - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Andreas full_name: Hohmann, Andreas last_name: Hohmann citation: ama: Dellnitz M, Hohmann A. A subdivision algorithm for the computation of unstable manifolds and global attractors. Numerische Mathematik. 1997;75:293-317. doi:10.1007/s002110050240 apa: Dellnitz, M., & Hohmann, A. (1997). A subdivision algorithm for the computation of unstable manifolds and global attractors. Numerische Mathematik, 75, 293–317. https://doi.org/10.1007/s002110050240 bibtex: '@article{Dellnitz_Hohmann_1997, title={A subdivision algorithm for the computation of unstable manifolds and global attractors}, volume={75}, DOI={10.1007/s002110050240}, journal={Numerische Mathematik}, author={Dellnitz, Michael and Hohmann, Andreas}, year={1997}, pages={293–317} }' chicago: 'Dellnitz, Michael, and Andreas Hohmann. “A Subdivision Algorithm for the Computation of Unstable Manifolds and Global Attractors.” Numerische Mathematik 75 (1997): 293–317. https://doi.org/10.1007/s002110050240.' ieee: M. Dellnitz and A. Hohmann, “A subdivision algorithm for the computation of unstable manifolds and global attractors,” Numerische Mathematik, vol. 75, pp. 293–317, 1997. mla: Dellnitz, Michael, and Andreas Hohmann. “A Subdivision Algorithm for the Computation of Unstable Manifolds and Global Attractors.” Numerische Mathematik, vol. 75, 1997, pp. 293–317, doi:10.1007/s002110050240. short: M. Dellnitz, A. Hohmann, Numerische Mathematik 75 (1997) 293–317. date_created: 2020-05-19T09:07:27Z date_updated: 2022-01-06T06:53:02Z department: - _id: '101' doi: 10.1007/s002110050240 intvolume: ' 75' language: - iso: eng page: 293-317 publication: Numerische Mathematik publication_identifier: issn: - 0029-599X - 0945-3245 publication_status: published status: public title: A subdivision algorithm for the computation of unstable manifolds and global attractors type: journal_article user_id: '32643' volume: 75 year: '1997' ... --- _id: '16533' author: - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Andreas full_name: Hohmann, Andreas last_name: Hohmann citation: ama: 'Dellnitz M, Hohmann A. The Computation of Unstable Manifolds Using Subdivision and Continuation. In: Nonlinear Dynamical Systems and Chaos. Basel; 1996. doi:10.1007/978-3-0348-7518-9_21' apa: Dellnitz, M., & Hohmann, A. (1996). The Computation of Unstable Manifolds Using Subdivision and Continuation. In Nonlinear Dynamical Systems and Chaos. Basel. https://doi.org/10.1007/978-3-0348-7518-9_21 bibtex: '@inbook{Dellnitz_Hohmann_1996, place={Basel}, title={The Computation of Unstable Manifolds Using Subdivision and Continuation}, DOI={10.1007/978-3-0348-7518-9_21}, booktitle={Nonlinear Dynamical Systems and Chaos}, author={Dellnitz, Michael and Hohmann, Andreas}, year={1996} }' chicago: Dellnitz, Michael, and Andreas Hohmann. “The Computation of Unstable Manifolds Using Subdivision and Continuation.” In Nonlinear Dynamical Systems and Chaos. Basel, 1996. https://doi.org/10.1007/978-3-0348-7518-9_21. ieee: M. Dellnitz and A. Hohmann, “The Computation of Unstable Manifolds Using Subdivision and Continuation,” in Nonlinear Dynamical Systems and Chaos, Basel, 1996. mla: Dellnitz, Michael, and Andreas Hohmann. “The Computation of Unstable Manifolds Using Subdivision and Continuation.” Nonlinear Dynamical Systems and Chaos, 1996, doi:10.1007/978-3-0348-7518-9_21. short: 'M. Dellnitz, A. Hohmann, in: Nonlinear Dynamical Systems and Chaos, Basel, 1996.' date_created: 2020-04-15T08:27:35Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1007/978-3-0348-7518-9_21 language: - iso: eng place: Basel publication: Nonlinear Dynamical Systems and Chaos publication_identifier: isbn: - '9783034875202' - '9783034875189' publication_status: published status: public title: The Computation of Unstable Manifolds Using Subdivision and Continuation type: book_chapter user_id: '15701' year: '1996' ... --- _id: '16510' abstract: - lang: eng text: In an array of coupled oscillators, synchronous chaos may occur in the sense that all the oscillators behave identically although the corresponding motion is chaotic. When a parameter is varied this fully symmetric dynamical state can lose its stability, and the main purpose of this paper is to investigate which type of dynamical behavior is expected to be observed once the loss of stability has occurred. The essential tool is a classification of Lyapunov exponents based on the symmetry of the underlying problem. This classification is crucial in the derivation of the analytical results but it also allows an efficient computation of the dominant Lyapunov exponent associated with each symmetry type. We show how these dominant exponents determine the stability of invariant sets possessing various instantaneous symmetries, and this leads to the idea of symmetry breaking bifurcations of chaotic attractors. Finally, the results and ideas are illustrated for several systems of coupled oscillators. author: - first_name: Philip J. full_name: Aston, Philip J. last_name: Aston - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz citation: ama: Aston PJ, Dellnitz M. Symmetry Breaking Bifurcations of Chaotic Attractors. International Journal of Bifurcation and Chaos. 1995:1643-1676. doi:10.1142/s021812749500123x apa: Aston, P. J., & Dellnitz, M. (1995). Symmetry Breaking Bifurcations of Chaotic Attractors. International Journal of Bifurcation and Chaos, 1643–1676. https://doi.org/10.1142/s021812749500123x bibtex: '@article{Aston_Dellnitz_1995, title={Symmetry Breaking Bifurcations of Chaotic Attractors}, DOI={10.1142/s021812749500123x}, journal={International Journal of Bifurcation and Chaos}, author={Aston, Philip J. and Dellnitz, Michael}, year={1995}, pages={1643–1676} }' chicago: Aston, Philip J., and Michael Dellnitz. “Symmetry Breaking Bifurcations of Chaotic Attractors.” International Journal of Bifurcation and Chaos, 1995, 1643–76. https://doi.org/10.1142/s021812749500123x. ieee: P. J. Aston and M. Dellnitz, “Symmetry Breaking Bifurcations of Chaotic Attractors,” International Journal of Bifurcation and Chaos, pp. 1643–1676, 1995. mla: Aston, Philip J., and Michael Dellnitz. “Symmetry Breaking Bifurcations of Chaotic Attractors.” International Journal of Bifurcation and Chaos, 1995, pp. 1643–76, doi:10.1142/s021812749500123x. short: P.J. Aston, M. Dellnitz, International Journal of Bifurcation and Chaos (1995) 1643–1676. date_created: 2020-04-15T07:23:50Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1142/s021812749500123x language: - iso: eng page: 1643-1676 publication: International Journal of Bifurcation and Chaos publication_identifier: issn: - 0218-1274 - 1793-6551 publication_status: published status: public title: Symmetry Breaking Bifurcations of Chaotic Attractors type: journal_article user_id: '15701' year: '1995' ... --- _id: '16532' author: - first_name: M full_name: Dellnitz, M last_name: Dellnitz - first_name: C full_name: Heinrich, C last_name: Heinrich citation: ama: Dellnitz M, Heinrich C. Admissible symmetry increasing bifurcations. Nonlinearity. 1995:1039-1066. doi:10.1088/0951-7715/8/6/009 apa: Dellnitz, M., & Heinrich, C. (1995). Admissible symmetry increasing bifurcations. Nonlinearity, 1039–1066. https://doi.org/10.1088/0951-7715/8/6/009 bibtex: '@article{Dellnitz_Heinrich_1995, title={Admissible symmetry increasing bifurcations}, DOI={10.1088/0951-7715/8/6/009}, journal={Nonlinearity}, author={Dellnitz, M and Heinrich, C}, year={1995}, pages={1039–1066} }' chicago: Dellnitz, M, and C Heinrich. “Admissible Symmetry Increasing Bifurcations.” Nonlinearity, 1995, 1039–66. https://doi.org/10.1088/0951-7715/8/6/009. ieee: M. Dellnitz and C. Heinrich, “Admissible symmetry increasing bifurcations,” Nonlinearity, pp. 1039–1066, 1995. mla: Dellnitz, M., and C. Heinrich. “Admissible Symmetry Increasing Bifurcations.” Nonlinearity, 1995, pp. 1039–66, doi:10.1088/0951-7715/8/6/009. short: M. Dellnitz, C. Heinrich, Nonlinearity (1995) 1039–1066. date_created: 2020-04-15T08:25:12Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1088/0951-7715/8/6/009 language: - iso: eng page: 1039-1066 publication: Nonlinearity publication_identifier: issn: - 0951-7715 - 1361-6544 publication_status: published status: public title: Admissible symmetry increasing bifurcations type: journal_article user_id: '15701' year: '1995' ... --- _id: '16542' author: - first_name: M full_name: Dellnitz, M last_name: Dellnitz - first_name: I full_name: Melbourne, I last_name: Melbourne citation: ama: Dellnitz M, Melbourne I. A note on the shadowing lemma and symmetric periodic points. Nonlinearity. 1995:1067-1075. doi:10.1088/0951-7715/8/6/010 apa: Dellnitz, M., & Melbourne, I. (1995). A note on the shadowing lemma and symmetric periodic points. Nonlinearity, 1067–1075. https://doi.org/10.1088/0951-7715/8/6/010 bibtex: '@article{Dellnitz_Melbourne_1995, title={A note on the shadowing lemma and symmetric periodic points}, DOI={10.1088/0951-7715/8/6/010}, journal={Nonlinearity}, author={Dellnitz, M and Melbourne, I}, year={1995}, pages={1067–1075} }' chicago: Dellnitz, M, and I Melbourne. “A Note on the Shadowing Lemma and Symmetric Periodic Points.” Nonlinearity, 1995, 1067–75. https://doi.org/10.1088/0951-7715/8/6/010. ieee: M. Dellnitz and I. Melbourne, “A note on the shadowing lemma and symmetric periodic points,” Nonlinearity, pp. 1067–1075, 1995. mla: Dellnitz, M., and I. Melbourne. “A Note on the Shadowing Lemma and Symmetric Periodic Points.” Nonlinearity, 1995, pp. 1067–75, doi:10.1088/0951-7715/8/6/010. short: M. Dellnitz, I. Melbourne, Nonlinearity (1995) 1067–1075. date_created: 2020-04-15T08:46:30Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1088/0951-7715/8/6/010 language: - iso: eng page: 1067-1075 publication: Nonlinearity publication_identifier: issn: - 0951-7715 - 1361-6544 publication_status: published status: public title: A note on the shadowing lemma and symmetric periodic points type: journal_article user_id: '15701' year: '1995' ... --- _id: '16550' author: - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Michael full_name: Field, Michael last_name: Field - first_name: Martin full_name: Golubitsky, Martin last_name: Golubitsky - first_name: Jun full_name: Ma, Jun last_name: Ma - first_name: Andreas full_name: Hohmann, Andreas last_name: Hohmann citation: ama: Dellnitz M, Field M, Golubitsky M, Ma J, Hohmann A. Cycling Chaos. International Journal of Bifurcation and Chaos. 1995:1243-1247. doi:10.1142/s0218127495000909 apa: Dellnitz, M., Field, M., Golubitsky, M., Ma, J., & Hohmann, A. (1995). Cycling Chaos. International Journal of Bifurcation and Chaos, 1243–1247. https://doi.org/10.1142/s0218127495000909 bibtex: '@article{Dellnitz_Field_Golubitsky_Ma_Hohmann_1995, title={Cycling Chaos}, DOI={10.1142/s0218127495000909}, journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael and Field, Michael and Golubitsky, Martin and Ma, Jun and Hohmann, Andreas}, year={1995}, pages={1243–1247} }' chicago: Dellnitz, Michael, Michael Field, Martin Golubitsky, Jun Ma, and Andreas Hohmann. “Cycling Chaos.” International Journal of Bifurcation and Chaos, 1995, 1243–47. https://doi.org/10.1142/s0218127495000909. ieee: M. Dellnitz, M. Field, M. Golubitsky, J. Ma, and A. Hohmann, “Cycling Chaos,” International Journal of Bifurcation and Chaos, pp. 1243–1247, 1995. mla: Dellnitz, Michael, et al. “Cycling Chaos.” International Journal of Bifurcation and Chaos, 1995, pp. 1243–47, doi:10.1142/s0218127495000909. short: M. Dellnitz, M. Field, M. Golubitsky, J. Ma, A. Hohmann, International Journal of Bifurcation and Chaos (1995) 1243–1247. date_created: 2020-04-15T09:04:16Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1142/s0218127495000909 language: - iso: eng page: 1243-1247 publication: International Journal of Bifurcation and Chaos publication_identifier: issn: - 0218-1274 - 1793-6551 publication_status: published status: public title: Cycling Chaos type: journal_article user_id: '15701' year: '1995' ... --- _id: '16551' abstract: - lang: eng text: Spiral patterns have been observed experimentally, numerically, and theoretically in a variety of systems. It is often believed that these spiral wave patterns can occur only in systems of reaction–diffusion equations. We show, both theoretically (using Hopf bifurcation techniques) and numerically (using both direct simulation and continuation of rotating waves) that spiral wave patterns can appear in a single reaction–diffusion equation [ in u(x, t)] on a disk, if one assumes "spiral" boundary conditions (ur = muθ). Spiral boundary conditions are motivated by assuming that a solution is infinitesimally an Archimedian spiral near the boundary. It follows from a bifurcation analysis that for this form of spirals there are no singularities in the spiral pattern (technically there is no spiral tip) and that at bifurcation there is a steep gradient between the "red" and "blue" arms of the spiral. author: - first_name: Michael full_name: Dellnitz, Michael last_name: Dellnitz - first_name: Martin full_name: Golubitsky, Martin last_name: Golubitsky - first_name: Andreas full_name: Hohmann, Andreas last_name: Hohmann - first_name: Ian full_name: Stewart, Ian last_name: Stewart citation: ama: Dellnitz M, Golubitsky M, Hohmann A, Stewart I. Spirals in Scalar Reaction–Diffusion Equations. International Journal of Bifurcation and Chaos. 1995:1487-1501. doi:10.1142/s0218127495001149 apa: Dellnitz, M., Golubitsky, M., Hohmann, A., & Stewart, I. (1995). Spirals in Scalar Reaction–Diffusion Equations. International Journal of Bifurcation and Chaos, 1487–1501. https://doi.org/10.1142/s0218127495001149 bibtex: '@article{Dellnitz_Golubitsky_Hohmann_Stewart_1995, title={Spirals in Scalar Reaction–Diffusion Equations}, DOI={10.1142/s0218127495001149}, journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael and Golubitsky, Martin and Hohmann, Andreas and Stewart, Ian}, year={1995}, pages={1487–1501} }' chicago: Dellnitz, Michael, Martin Golubitsky, Andreas Hohmann, and Ian Stewart. “Spirals in Scalar Reaction–Diffusion Equations.” International Journal of Bifurcation and Chaos, 1995, 1487–1501. https://doi.org/10.1142/s0218127495001149. ieee: M. Dellnitz, M. Golubitsky, A. Hohmann, and I. Stewart, “Spirals in Scalar Reaction–Diffusion Equations,” International Journal of Bifurcation and Chaos, pp. 1487–1501, 1995. mla: Dellnitz, Michael, et al. “Spirals in Scalar Reaction–Diffusion Equations.” International Journal of Bifurcation and Chaos, 1995, pp. 1487–501, doi:10.1142/s0218127495001149. short: M. Dellnitz, M. Golubitsky, A. Hohmann, I. Stewart, International Journal of Bifurcation and Chaos (1995) 1487–1501. date_created: 2020-04-15T09:05:30Z date_updated: 2022-01-06T06:52:52Z department: - _id: '101' doi: 10.1142/s0218127495001149 language: - iso: eng page: 1487-1501 publication: International Journal of Bifurcation and Chaos publication_identifier: issn: - 0218-1274 - 1793-6551 publication_status: published status: public title: Spirals in Scalar Reaction–Diffusion Equations type: journal_article user_id: '15701' year: '1995' ...