Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Symbolic dynamics for nonhyperbolic systems

Author(s): David Richeson; Jim Wiseman
Journal: Proc. Amer. Math. Soc. 138 (2010), 4373-4385.
MSC (2010): Primary 37B30, 37B10; Secondary 37M99
Posted: May 27, 2010
MathSciNet review: 2680062
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We introduce index systems, a tool for studying isolated invariant sets of dynamical systems that are not necessarily hyperbolic. The mapping of the index systems mimics the expansion and contraction of hyperbolic maps on the tangent space, and they may be used like Markov partitions to generate symbolic dynamics. Every continuous dynamical system satisfying a weak form of expansiveness possesses an index system. Because of their topological robustness, they can be used to obtain rigorous results from computer approximations of a dynamical system.

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