@inbook{16513,
  author       = {{Aston, P. J. and Dellnitz, M.}},
  booktitle    = {{Equadiff 99}},
  isbn         = {{9789810243593}},
  title        = {{{The Computation of Lyapunov Exponents via Spatial Integration Using Vector Norms}}},
  doi          = {{10.1142/9789812792617_0196}},
  year         = {{2000}},
}

@inbook{16553,
  author       = {{Dellnitz, Michael and Froyland, Gary and Sertl, Stefan}},
  booktitle    = {{Equadiff 99}},
  isbn         = {{9789810243593}},
  title        = {{{A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius Operator}}},
  doi          = {{10.1142/9789812792617_0199}},
  year         = {{2000}},
}

@article{16554,
  author       = {{Dellnitz, Michael and Froyland, Gary and Sertl, Stefan}},
  issn         = {{0951-7715}},
  journal      = {{Nonlinearity}},
  pages        = {{1171--1188}},
  title        = {{{On the isolated spectrum of the Perron-Frobenius operator}}},
  doi          = {{10.1088/0951-7715/13/4/310}},
  year         = {{2000}},
}

@inbook{16616,
  author       = {{Junge, Oliver}},
  booktitle    = {{Equadiff 99}},
  isbn         = {{9789810243593}},
  title        = {{{Rigorous discretization of subdivision techniques}}},
  doi          = {{10.1142/9789812792617_0178}},
  year         = {{2000}},
}

@inbook{17018,
  author       = {{Dellnitz, Michael and Junge, Oliver and Rumpf, Martin and Strzodka, Robert}},
  booktitle    = {{Equadiff 99}},
  isbn         = {{9789810243593}},
  pages        = {{1053----1059}},
  title        = {{{The computation of an unstable invariant set inside a cylinder containing a knotted flow}}},
  doi          = {{10.1142/9789812792617_0204}},
  year         = {{2000}},
}

@article{16511,
  author       = {{Aston, Philip J. and Dellnitz, Michael}},
  issn         = {{0045-7825}},
  journal      = {{Computer Methods in Applied Mechanics and Engineering}},
  pages        = {{223--237}},
  title        = {{{The computation of lyapunov exponents via spatial integration with application to blowout bifurcations}}},
  doi          = {{10.1016/s0045-7825(98)00196-0}},
  year         = {{1999}},
}

@article{16537,
  author       = {{Dellnitz, Michael and Junge, Oliver}},
  issn         = {{0036-1429}},
  journal      = {{SIAM Journal on Numerical Analysis}},
  pages        = {{491--515}},
  title        = {{{On the Approximation of Complicated Dynamical Behavior}}},
  doi          = {{10.1137/s0036142996313002}},
  year         = {{1999}},
}

@inbook{16584,
  author       = {{Deuflhard, Peter and Dellnitz, Michael and Junge, Oliver and Schütte, Christof}},
  booktitle    = {{Computational Molecular Dynamics: Challenges, Methods, Ideas}},
  isbn         = {{9783540632429}},
  issn         = {{1439-7358}},
  title        = {{{Computation of Essential Molecular Dynamics by Subdivision Techniques}}},
  doi          = {{10.1007/978-3-642-58360-5_5}},
  year         = {{1999}},
}

@article{17017,
  author       = {{Bürkle, David and Dellnitz, Michael and Junge, Oliver and Rumpf, Martin and Spielberg, Michael}},
  journal      = {{Proceedings of Visualization 99}},
  title        = {{{Visualizing Complicated Dynamics}}},
  year         = {{1999}},
}

@article{16536,
  author       = {{Dellnitz, Michael and Junge, Oliver}},
  issn         = {{1432-9360}},
  journal      = {{Computing and Visualization in Science}},
  pages        = {{63--68}},
  title        = {{{An adaptive subdivision technique for the approximation of attractors and invariant measures}}},
  doi          = {{10.1007/s007910050006}},
  year         = {{1998}},
}

@article{16535,
  abstract     = {{<jats:p> 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. </jats:p>}},
  author       = {{Dellnitz, Michael and Junge, Oliver}},
  issn         = {{0218-1274}},
  journal      = {{International Journal of Bifurcation and Chaos}},
  pages        = {{2475--2485}},
  title        = {{{Almost Invariant Sets in Chua's Circuit}}},
  doi          = {{10.1142/s0218127497001655}},
  year         = {{1997}},
}

@article{16552,
  author       = {{Dellnitz, Michael and Hohmann, Andreas and Junge, Oliver and Rumpf, Martin}},
  issn         = {{1054-1500}},
  journal      = {{Chaos: An Interdisciplinary Journal of Nonlinear Science}},
  pages        = {{221--228}},
  title        = {{{Exploring invariant sets and invariant measures}}},
  doi          = {{10.1063/1.166223}},
  year         = {{1997}},
}

@article{16614,
  author       = {{Guder, Rabbijah and Dellnitz, Michael and Kreuzer, Edwin}},
  issn         = {{0960-0779}},
  journal      = {{Chaos, Solitons & Fractals}},
  pages        = {{525--534}},
  title        = {{{An adaptive method for the approximation of the generalized cell mapping}}},
  doi          = {{10.1016/s0960-0779(96)00118-x}},
  year         = {{1997}},
}

@article{17015,
  author       = {{Dellnitz, Michael and Hohmann, Andreas}},
  issn         = {{0029-599X}},
  journal      = {{Numerische Mathematik}},
  pages        = {{293--317}},
  title        = {{{A subdivision algorithm for the computation of unstable manifolds and global attractors}}},
  doi          = {{10.1007/s002110050240}},
  volume       = {{75}},
  year         = {{1997}},
}

@inbook{16533,
  author       = {{Dellnitz, Michael and Hohmann, Andreas}},
  booktitle    = {{Nonlinear Dynamical Systems and Chaos}},
  isbn         = {{9783034875202}},
  title        = {{{The Computation of Unstable Manifolds Using Subdivision and Continuation}}},
  doi          = {{10.1007/978-3-0348-7518-9_21}},
  year         = {{1996}},
}

@article{16510,
  abstract     = {{<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>}},
  author       = {{Aston, Philip J. and Dellnitz, Michael}},
  issn         = {{0218-1274}},
  journal      = {{International Journal of Bifurcation and Chaos}},
  pages        = {{1643--1676}},
  title        = {{{Symmetry Breaking Bifurcations of Chaotic Attractors}}},
  doi          = {{10.1142/s021812749500123x}},
  year         = {{1995}},
}

@article{16532,
  author       = {{Dellnitz, M and Heinrich, C}},
  issn         = {{0951-7715}},
  journal      = {{Nonlinearity}},
  pages        = {{1039--1066}},
  title        = {{{Admissible symmetry increasing bifurcations}}},
  doi          = {{10.1088/0951-7715/8/6/009}},
  year         = {{1995}},
}

@article{16542,
  author       = {{Dellnitz, M and Melbourne, I}},
  issn         = {{0951-7715}},
  journal      = {{Nonlinearity}},
  pages        = {{1067--1075}},
  title        = {{{A note on the shadowing lemma and symmetric periodic points}}},
  doi          = {{10.1088/0951-7715/8/6/010}},
  year         = {{1995}},
}

@article{16550,
  author       = {{Dellnitz, Michael and Field, Michael and Golubitsky, Martin and Ma, Jun and Hohmann, Andreas}},
  issn         = {{0218-1274}},
  journal      = {{International Journal of Bifurcation and Chaos}},
  pages        = {{1243--1247}},
  title        = {{{Cycling Chaos}}},
  doi          = {{10.1142/s0218127495000909}},
  year         = {{1995}},
}

@article{16551,
  abstract     = {{<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>}},
  author       = {{Dellnitz, Michael and Golubitsky, Martin and Hohmann, Andreas and Stewart, Ian}},
  issn         = {{0218-1274}},
  journal      = {{International Journal of Bifurcation and Chaos}},
  pages        = {{1487--1501}},
  title        = {{{Spirals in Scalar Reaction–Diffusion Equations}}},
  doi          = {{10.1142/s0218127495001149}},
  year         = {{1995}},
}