[{"publication_status":"published","year":"1996","intvolume":"        24","page":"433-444","citation":{"apa":"Hilgert, J., &#38; Neeb, K.-H. (1996). Orthogonal Lie Algrebras with Cone Potential. <i>Commun. in Alg.</i>, <i>24</i>, 433–444.","short":"J. Hilgert, K.-H. Neeb, Commun. in Alg. 24 (1996) 433–444.","bibtex":"@article{Hilgert_Neeb_1996, title={Orthogonal Lie Algrebras with Cone Potential}, volume={24}, journal={Commun. in Alg.}, author={Hilgert, Joachim and Neeb, K.-H.}, year={1996}, pages={433–444} }","mla":"Hilgert, Joachim, and K. H. Neeb. “Orthogonal Lie Algrebras with Cone Potential.” <i>Commun. in Alg.</i>, vol. 24, 1996, pp. 433–44.","ieee":"J. Hilgert and K.-H. Neeb, “Orthogonal Lie Algrebras with Cone Potential,” <i>Commun. in Alg.</i>, vol. 24, pp. 433–444, 1996.","chicago":"Hilgert, Joachim, and K.-H. Neeb. “Orthogonal Lie Algrebras with Cone Potential.” <i>Commun. in Alg.</i> 24 (1996): 433–44.","ama":"Hilgert J, Neeb K-H. Orthogonal Lie Algrebras with Cone Potential. <i>Commun in Alg</i>. 1996;24:433-444."},"date_updated":"2024-02-20T13:32:12Z","volume":24,"author":[{"first_name":"Joachim","last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220"},{"first_name":"K.-H.","full_name":"Neeb, K.-H.","last_name":"Neeb"}],"date_created":"2024-02-19T07:23:45Z","title":"Orthogonal Lie Algrebras with Cone Potential","publication":"Commun. in Alg.","type":"journal_article","status":"public","_id":"51431","department":[{"_id":"91"}],"user_id":"49063","language":[{"iso":"eng"}],"extern":"1"},{"type":"journal_article","publication":"J. Funct. Anal.","status":"public","_id":"51428","user_id":"49063","department":[{"_id":"91"}],"extern":"1","language":[{"iso":"eng"}],"publication_status":"published","year":"1996","citation":{"ama":"Hilgert J, Neeb K-H. Spherical Functions on Olshanskii Spaces. <i>J Funct Anal</i>. 1996;142:446-493.","ieee":"J. Hilgert and K.-H. Neeb, “Spherical Functions on Olshanskii Spaces,” <i>J. Funct. Anal.</i>, vol. 142, pp. 446–493, 1996.","chicago":"Hilgert, Joachim, and K.-H. Neeb. “Spherical Functions on Olshanskii Spaces.” <i>J. Funct. Anal.</i> 142 (1996): 446–93.","bibtex":"@article{Hilgert_Neeb_1996, title={Spherical Functions on Olshanskii Spaces}, volume={142}, journal={J. Funct. Anal.}, author={Hilgert, Joachim and Neeb, K.-H.}, year={1996}, pages={446–493} }","mla":"Hilgert, Joachim, and K. H. Neeb. “Spherical Functions on Olshanskii Spaces.” <i>J. Funct. Anal.</i>, vol. 142, 1996, pp. 446–93.","short":"J. Hilgert, K.-H. Neeb, J. Funct. Anal. 142 (1996) 446–493.","apa":"Hilgert, J., &#38; Neeb, K.-H. (1996). Spherical Functions on Olshanskii Spaces. <i>J. Funct. Anal.</i>, <i>142</i>, 446–493."},"intvolume":"       142","page":"446-493","date_updated":"2024-02-20T13:32:17Z","author":[{"last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220","first_name":"Joachim"},{"first_name":"K.-H.","last_name":"Neeb","full_name":"Neeb, K.-H."}],"date_created":"2024-02-19T07:21:03Z","volume":142,"title":"Spherical Functions on Olshanskii Spaces"},{"citation":{"ieee":"J. Hilgert, “Knapp, A.W. Lie Groups Beyond an Introduction  (Birkhäuser, Boston, 1996),” <i>Zentralblatt für Math.</i> 1996.","chicago":"Hilgert, Joachim. “Knapp, A.W. Lie Groups Beyond an Introduction  (Birkhäuser, Boston, 1996).” <i>Zentralblatt Für Math.</i>, 1996.","ama":"Hilgert J. Knapp, A.W. Lie Groups Beyond an Introduction  (Birkhäuser, Boston, 1996). <i>Zentralblatt für Math</i>. Published online 1996.","short":"J. Hilgert, Zentralblatt Für Math. (1996).","mla":"Hilgert, Joachim. “Knapp, A.W. Lie Groups Beyond an Introduction  (Birkhäuser, Boston, 1996).” <i>Zentralblatt Für Math.</i>, 1996.","bibtex":"@article{Hilgert_1996, title={Knapp, A.W. Lie Groups Beyond an Introduction  (Birkhäuser, Boston, 1996)}, journal={Zentralblatt für Math.}, author={Hilgert, Joachim}, year={1996} }","apa":"Hilgert, J. (1996). Knapp, A.W. Lie Groups Beyond an Introduction  (Birkhäuser, Boston, 1996). In <i>Zentralblatt für Math.</i>"},"year":"1996","publication_status":"published","title":"Knapp, A.W. Lie Groups Beyond an Introduction  (Birkhäuser, Boston, 1996)","date_created":"2024-02-20T13:40:21Z","author":[{"first_name":"Joachim","id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert"}],"date_updated":"2024-02-20T13:40:25Z","status":"public","type":"review","publication":"Zentralblatt für Math.","language":[{"iso":"eng"}],"extern":"1","user_id":"49063","department":[{"_id":"91"}],"_id":"51597"},{"language":[{"iso":"eng"}],"extern":"1","_id":"44544","user_id":"49063","department":[{"_id":"602"}],"status":"public","type":"journal_article","publication":"U sviti Mathematyky","title":"Euler’s theorem and map color problems","date_updated":"2023-05-07T01:35:38Z","author":[{"first_name":"Igor","full_name":"Burban, Igor","id":"72064","last_name":"Burban"}],"date_created":"2023-05-07T01:03:07Z","volume":2,"year":"1996","citation":{"apa":"Burban, I. (1996). Euler’s theorem and map color problems. <i>U Sviti Mathematyky</i>, <i>2</i>(2).","short":"I. Burban, U Sviti Mathematyky 2 (1996).","mla":"Burban, Igor. “Euler’s Theorem and Map Color Problems.” <i>U Sviti Mathematyky</i>, vol. 2, no. 2, 1996.","bibtex":"@article{Burban_1996, title={Euler’s theorem and map color problems}, volume={2}, number={2}, journal={U sviti Mathematyky}, author={Burban, Igor}, year={1996} }","chicago":"Burban, Igor. “Euler’s Theorem and Map Color Problems.” <i>U Sviti Mathematyky</i> 2, no. 2 (1996).","ieee":"I. Burban, “Euler’s theorem and map color problems,” <i>U sviti Mathematyky</i>, vol. 2, no. 2, 1996.","ama":"Burban I. Euler’s theorem and map color problems. <i>U sviti Mathematyky</i>. 1996;2(2)."},"intvolume":"         2","publication_status":"published","issue":"2"},{"date_updated":"2023-05-07T01:36:26Z","volume":2,"date_created":"2023-05-07T01:02:11Z","author":[{"first_name":"Igor","last_name":"Burban","full_name":"Burban, Igor","id":"72064"}],"title":"Solutions of equations in integers","publication_status":"published","issue":"4","year":"1996","intvolume":"         2","citation":{"bibtex":"@article{Burban_1996, title={Solutions of equations in integers}, volume={2}, number={4}, journal={U sviti Mathematyky}, author={Burban, Igor}, year={1996} }","mla":"Burban, Igor. “Solutions of Equations in Integers.” <i>U Sviti Mathematyky</i>, vol. 2, no. 4, 1996.","short":"I. Burban, U Sviti Mathematyky 2 (1996).","apa":"Burban, I. (1996). Solutions of equations in integers. <i>U Sviti Mathematyky</i>, <i>2</i>(4).","ama":"Burban I. Solutions of equations in integers. <i>U sviti Mathematyky</i>. 1996;2(4).","chicago":"Burban, Igor. “Solutions of Equations in Integers.” <i>U Sviti Mathematyky</i> 2, no. 4 (1996).","ieee":"I. Burban, “Solutions of equations in integers,” <i>U sviti Mathematyky</i>, vol. 2, no. 4, 1996."},"_id":"44543","department":[{"_id":"602"}],"user_id":"49063","extern":"1","language":[{"iso":"eng"}],"publication":"U sviti Mathematyky","type":"journal_article","status":"public"},{"publication":"Journal of Lie Theory","language":[{"iso":"eng"}],"keyword":["22E35","22E50","28C10"],"issue":"2","quality_controlled":"1","year":"1996","date_created":"2026-02-26T13:33:20Z","title":"Haar measure on linear groups over local skew fields","type":"journal_article","status":"public","user_id":"178","department":[{"_id":"10"},{"_id":"87"},{"_id":"93"}],"_id":"64730","extern":"1","article_type":"original","publication_identifier":{"issn":["0949-5932"]},"citation":{"chicago":"Glöckner, Helge. “Haar Measure on Linear Groups over Local Skew Fields.” <i>Journal of Lie Theory</i> 6, no. 2 (1996): 165–177.","ieee":"H. Glöckner, “Haar measure on linear groups over local skew fields,” <i>Journal of Lie Theory</i>, vol. 6, no. 2, pp. 165–177, 1996.","ama":"Glöckner H. Haar measure on linear groups over local skew fields. <i>Journal of Lie Theory</i>. 1996;6(2):165–177.","bibtex":"@article{Glöckner_1996, title={Haar measure on linear groups over local skew fields}, volume={6}, number={2}, journal={Journal of Lie Theory}, author={Glöckner, Helge}, year={1996}, pages={165–177} }","short":"H. Glöckner, Journal of Lie Theory 6 (1996) 165–177.","mla":"Glöckner, Helge. “Haar Measure on Linear Groups over Local Skew Fields.” <i>Journal of Lie Theory</i>, vol. 6, no. 2, 1996, pp. 165–177.","apa":"Glöckner, H. (1996). Haar measure on linear groups over local skew fields. <i>Journal of Lie Theory</i>, <i>6</i>(2), 165–177."},"page":"165–177","intvolume":"         6","author":[{"first_name":"Helge","full_name":"Glöckner, Helge","id":"178","last_name":"Glöckner"}],"volume":6,"date_updated":"2026-02-27T07:36:58Z"},{"status":"public","abstract":[{"lang":"eng","text":"<jats:p> 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. </jats:p>"}],"type":"journal_article","publication":"International Journal of Bifurcation and Chaos","language":[{"iso":"eng"}],"user_id":"15701","department":[{"_id":"101"}],"_id":"16510","citation":{"ama":"Aston PJ, Dellnitz M. Symmetry Breaking Bifurcations of Chaotic Attractors. <i>International Journal of Bifurcation and Chaos</i>. 1995:1643-1676. doi:<a href=\"https://doi.org/10.1142/s021812749500123x\">10.1142/s021812749500123x</a>","ieee":"P. J. Aston and M. Dellnitz, “Symmetry Breaking Bifurcations of Chaotic Attractors,” <i>International Journal of Bifurcation and Chaos</i>, pp. 1643–1676, 1995.","chicago":"Aston, Philip J., and Michael Dellnitz. “Symmetry Breaking Bifurcations of Chaotic Attractors.” <i>International Journal of Bifurcation and Chaos</i>, 1995, 1643–76. <a href=\"https://doi.org/10.1142/s021812749500123x\">https://doi.org/10.1142/s021812749500123x</a>.","apa":"Aston, P. J., &#38; Dellnitz, M. (1995). Symmetry Breaking Bifurcations of Chaotic Attractors. <i>International Journal of Bifurcation and Chaos</i>, 1643–1676. <a href=\"https://doi.org/10.1142/s021812749500123x\">https://doi.org/10.1142/s021812749500123x</a>","short":"P.J. Aston, M. Dellnitz, International Journal of Bifurcation and Chaos (1995) 1643–1676.","bibtex":"@article{Aston_Dellnitz_1995, title={Symmetry Breaking Bifurcations of Chaotic Attractors}, DOI={<a href=\"https://doi.org/10.1142/s021812749500123x\">10.1142/s021812749500123x</a>}, journal={International Journal of Bifurcation and Chaos}, author={Aston, Philip J. and Dellnitz, Michael}, year={1995}, pages={1643–1676} }","mla":"Aston, Philip J., and Michael Dellnitz. “Symmetry Breaking Bifurcations of Chaotic Attractors.” <i>International Journal of Bifurcation and Chaos</i>, 1995, pp. 1643–76, doi:<a href=\"https://doi.org/10.1142/s021812749500123x\">10.1142/s021812749500123x</a>."},"page":"1643-1676","year":"1995","publication_status":"published","publication_identifier":{"issn":["0218-1274","1793-6551"]},"doi":"10.1142/s021812749500123x","title":"Symmetry Breaking Bifurcations of Chaotic Attractors","author":[{"first_name":"Philip J.","full_name":"Aston, Philip J.","last_name":"Aston"},{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"}],"date_created":"2020-04-15T07:23:50Z","date_updated":"2022-01-06T06:52:52Z"},{"type":"journal_article","publication":"Nonlinearity","status":"public","_id":"16532","user_id":"15701","department":[{"_id":"101"}],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"year":"1995","citation":{"chicago":"Dellnitz, M, and C Heinrich. “Admissible Symmetry Increasing Bifurcations.” <i>Nonlinearity</i>, 1995, 1039–66. <a href=\"https://doi.org/10.1088/0951-7715/8/6/009\">https://doi.org/10.1088/0951-7715/8/6/009</a>.","ieee":"M. Dellnitz and C. Heinrich, “Admissible symmetry increasing bifurcations,” <i>Nonlinearity</i>, pp. 1039–1066, 1995.","ama":"Dellnitz M, Heinrich C. Admissible symmetry increasing bifurcations. <i>Nonlinearity</i>. 1995:1039-1066. doi:<a href=\"https://doi.org/10.1088/0951-7715/8/6/009\">10.1088/0951-7715/8/6/009</a>","mla":"Dellnitz, M., and C. Heinrich. “Admissible Symmetry Increasing Bifurcations.” <i>Nonlinearity</i>, 1995, pp. 1039–66, doi:<a href=\"https://doi.org/10.1088/0951-7715/8/6/009\">10.1088/0951-7715/8/6/009</a>.","short":"M. Dellnitz, C. Heinrich, Nonlinearity (1995) 1039–1066.","bibtex":"@article{Dellnitz_Heinrich_1995, title={Admissible symmetry increasing bifurcations}, DOI={<a href=\"https://doi.org/10.1088/0951-7715/8/6/009\">10.1088/0951-7715/8/6/009</a>}, journal={Nonlinearity}, author={Dellnitz, M and Heinrich, C}, year={1995}, pages={1039–1066} }","apa":"Dellnitz, M., &#38; Heinrich, C. (1995). Admissible symmetry increasing bifurcations. <i>Nonlinearity</i>, 1039–1066. <a href=\"https://doi.org/10.1088/0951-7715/8/6/009\">https://doi.org/10.1088/0951-7715/8/6/009</a>"},"page":"1039-1066","date_updated":"2022-01-06T06:52:52Z","date_created":"2020-04-15T08:25:12Z","author":[{"first_name":"M","last_name":"Dellnitz","full_name":"Dellnitz, M"},{"first_name":"C","full_name":"Heinrich, C","last_name":"Heinrich"}],"title":"Admissible symmetry increasing bifurcations","doi":"10.1088/0951-7715/8/6/009"},{"status":"public","type":"journal_article","publication":"Nonlinearity","language":[{"iso":"eng"}],"user_id":"15701","department":[{"_id":"101"}],"_id":"16542","citation":{"ieee":"M. Dellnitz and I. Melbourne, “A note on the shadowing lemma and symmetric periodic points,” <i>Nonlinearity</i>, pp. 1067–1075, 1995.","chicago":"Dellnitz, M, and I Melbourne. “A Note on the Shadowing Lemma and Symmetric Periodic Points.” <i>Nonlinearity</i>, 1995, 1067–75. <a href=\"https://doi.org/10.1088/0951-7715/8/6/010\">https://doi.org/10.1088/0951-7715/8/6/010</a>.","ama":"Dellnitz M, Melbourne I. A note on the shadowing lemma and symmetric periodic points. <i>Nonlinearity</i>. 1995:1067-1075. doi:<a href=\"https://doi.org/10.1088/0951-7715/8/6/010\">10.1088/0951-7715/8/6/010</a>","short":"M. Dellnitz, I. Melbourne, Nonlinearity (1995) 1067–1075.","mla":"Dellnitz, M., and I. Melbourne. “A Note on the Shadowing Lemma and Symmetric Periodic Points.” <i>Nonlinearity</i>, 1995, pp. 1067–75, doi:<a href=\"https://doi.org/10.1088/0951-7715/8/6/010\">10.1088/0951-7715/8/6/010</a>.","bibtex":"@article{Dellnitz_Melbourne_1995, title={A note on the shadowing lemma and symmetric periodic points}, DOI={<a href=\"https://doi.org/10.1088/0951-7715/8/6/010\">10.1088/0951-7715/8/6/010</a>}, journal={Nonlinearity}, author={Dellnitz, M and Melbourne, I}, year={1995}, pages={1067–1075} }","apa":"Dellnitz, M., &#38; Melbourne, I. (1995). A note on the shadowing lemma and symmetric periodic points. <i>Nonlinearity</i>, 1067–1075. <a href=\"https://doi.org/10.1088/0951-7715/8/6/010\">https://doi.org/10.1088/0951-7715/8/6/010</a>"},"page":"1067-1075","year":"1995","publication_status":"published","publication_identifier":{"issn":["0951-7715","1361-6544"]},"doi":"10.1088/0951-7715/8/6/010","title":"A note on the shadowing lemma and symmetric periodic points","date_created":"2020-04-15T08:46:30Z","author":[{"full_name":"Dellnitz, M","last_name":"Dellnitz","first_name":"M"},{"first_name":"I","full_name":"Melbourne, I","last_name":"Melbourne"}],"date_updated":"2022-01-06T06:52:52Z"},{"language":[{"iso":"eng"}],"user_id":"15701","department":[{"_id":"101"}],"_id":"16550","status":"public","type":"journal_article","publication":"International Journal of Bifurcation and Chaos","doi":"10.1142/s0218127495000909","title":"Cycling Chaos","author":[{"full_name":"Dellnitz, Michael","last_name":"Dellnitz","first_name":"Michael"},{"last_name":"Field","full_name":"Field, Michael","first_name":"Michael"},{"full_name":"Golubitsky, Martin","last_name":"Golubitsky","first_name":"Martin"},{"last_name":"Ma","full_name":"Ma, Jun","first_name":"Jun"},{"full_name":"Hohmann, Andreas","last_name":"Hohmann","first_name":"Andreas"}],"date_created":"2020-04-15T09:04:16Z","date_updated":"2022-01-06T06:52:52Z","citation":{"apa":"Dellnitz, M., Field, M., Golubitsky, M., Ma, J., &#38; Hohmann, A. (1995). Cycling Chaos. <i>International Journal of Bifurcation and Chaos</i>, 1243–1247. <a href=\"https://doi.org/10.1142/s0218127495000909\">https://doi.org/10.1142/s0218127495000909</a>","short":"M. Dellnitz, M. Field, M. Golubitsky, J. Ma, A. Hohmann, International Journal of Bifurcation and Chaos (1995) 1243–1247.","bibtex":"@article{Dellnitz_Field_Golubitsky_Ma_Hohmann_1995, title={Cycling Chaos}, DOI={<a href=\"https://doi.org/10.1142/s0218127495000909\">10.1142/s0218127495000909</a>}, 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} }","mla":"Dellnitz, Michael, et al. “Cycling Chaos.” <i>International Journal of Bifurcation and Chaos</i>, 1995, pp. 1243–47, doi:<a href=\"https://doi.org/10.1142/s0218127495000909\">10.1142/s0218127495000909</a>.","ama":"Dellnitz M, Field M, Golubitsky M, Ma J, Hohmann A. Cycling Chaos. <i>International Journal of Bifurcation and Chaos</i>. 1995:1243-1247. doi:<a href=\"https://doi.org/10.1142/s0218127495000909\">10.1142/s0218127495000909</a>","ieee":"M. Dellnitz, M. Field, M. Golubitsky, J. Ma, and A. Hohmann, “Cycling Chaos,” <i>International Journal of Bifurcation and Chaos</i>, pp. 1243–1247, 1995.","chicago":"Dellnitz, Michael, Michael Field, Martin Golubitsky, Jun Ma, and Andreas Hohmann. “Cycling Chaos.” <i>International Journal of Bifurcation and Chaos</i>, 1995, 1243–47. <a href=\"https://doi.org/10.1142/s0218127495000909\">https://doi.org/10.1142/s0218127495000909</a>."},"page":"1243-1247","year":"1995","publication_status":"published","publication_identifier":{"issn":["0218-1274","1793-6551"]}},{"year":"1995","citation":{"ieee":"M. Dellnitz, M. Golubitsky, A. Hohmann, and I. Stewart, “Spirals in Scalar Reaction–Diffusion Equations,” <i>International Journal of Bifurcation and Chaos</i>, pp. 1487–1501, 1995.","chicago":"Dellnitz, Michael, Martin Golubitsky, Andreas Hohmann, and Ian Stewart. “Spirals in Scalar Reaction–Diffusion Equations.” <i>International Journal of Bifurcation and Chaos</i>, 1995, 1487–1501. <a href=\"https://doi.org/10.1142/s0218127495001149\">https://doi.org/10.1142/s0218127495001149</a>.","ama":"Dellnitz M, Golubitsky M, Hohmann A, Stewart I. Spirals in Scalar Reaction–Diffusion Equations. <i>International Journal of Bifurcation and Chaos</i>. 1995:1487-1501. doi:<a href=\"https://doi.org/10.1142/s0218127495001149\">10.1142/s0218127495001149</a>","bibtex":"@article{Dellnitz_Golubitsky_Hohmann_Stewart_1995, title={Spirals in Scalar Reaction–Diffusion Equations}, DOI={<a href=\"https://doi.org/10.1142/s0218127495001149\">10.1142/s0218127495001149</a>}, journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael and Golubitsky, Martin and Hohmann, Andreas and Stewart, Ian}, year={1995}, pages={1487–1501} }","short":"M. Dellnitz, M. Golubitsky, A. Hohmann, I. Stewart, International Journal of Bifurcation and Chaos (1995) 1487–1501.","mla":"Dellnitz, Michael, et al. “Spirals in Scalar Reaction–Diffusion Equations.” <i>International Journal of Bifurcation and Chaos</i>, 1995, pp. 1487–501, doi:<a href=\"https://doi.org/10.1142/s0218127495001149\">10.1142/s0218127495001149</a>.","apa":"Dellnitz, M., Golubitsky, M., Hohmann, A., &#38; Stewart, I. (1995). Spirals in Scalar Reaction–Diffusion Equations. <i>International Journal of Bifurcation and Chaos</i>, 1487–1501. <a href=\"https://doi.org/10.1142/s0218127495001149\">https://doi.org/10.1142/s0218127495001149</a>"},"page":"1487-1501","publication_status":"published","publication_identifier":{"issn":["0218-1274","1793-6551"]},"title":"Spirals in Scalar Reaction–Diffusion Equations","doi":"10.1142/s0218127495001149","date_updated":"2022-01-06T06:52:52Z","date_created":"2020-04-15T09:05:30Z","author":[{"last_name":"Dellnitz","full_name":"Dellnitz, Michael","first_name":"Michael"},{"last_name":"Golubitsky","full_name":"Golubitsky, Martin","first_name":"Martin"},{"first_name":"Andreas","full_name":"Hohmann, Andreas","last_name":"Hohmann"},{"first_name":"Ian","full_name":"Stewart, Ian","last_name":"Stewart"}],"abstract":[{"text":"<jats:p> 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 (u<jats:sub>r</jats:sub> = mu<jats:sub>θ</jats:sub>). 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. </jats:p>","lang":"eng"}],"status":"public","type":"journal_article","publication":"International Journal of Bifurcation and Chaos","language":[{"iso":"eng"}],"_id":"16551","user_id":"15701","department":[{"_id":"101"}]},{"user_id":"15701","department":[{"_id":"101"}],"_id":"16611","language":[{"iso":"eng"}],"type":"book_chapter","publication":"Normal Forms and Homoclinic Chaos","status":"public","date_created":"2020-04-16T08:02:13Z","author":[{"first_name":"Martin","full_name":"Golubitsky, Martin","last_name":"Golubitsky"},{"first_name":"Jerrold","full_name":"Marsden, Jerrold","last_name":"Marsden"},{"first_name":"Ian","last_name":"Stewart","full_name":"Stewart, Ian"},{"first_name":"Michael","full_name":"Dellnitz, Michael","last_name":"Dellnitz"}],"date_updated":"2022-01-06T06:52:53Z","doi":"10.1090/fic/004/05","title":"The constrained Liapunov-Schmidt procedure and periodic orbits","publication_status":"published","publication_identifier":{"isbn":["9780821803264","9781470429720"]},"citation":{"apa":"Golubitsky, M., Marsden, J., Stewart, I., &#38; Dellnitz, M. 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