Symbolic dynamics for nonhyperbolic systems
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- by David Richeson and Jim Wiseman PDF
- Proc. Amer. Math. Soc. 138 (2010), 4373-4385 Request permission
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.References
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Additional Information
- David Richeson
- Affiliation: Department of Mathematics and Computer Science, Dickinson College, Carlisle, Pennsylvania 17013
- MR Author ID: 642588
- ORCID: setImmediate$0.3081954432672045$9
- Email: richesod@dickinson.edu
- Jim Wiseman
- Affiliation: Department of Mathematics, Agnes Scott College, Decatur, Georgia 30030
- MR Author ID: 668909
- Email: jwiseman@agnesscott.edu
- Received by editor(s): September 4, 2009
- Received by editor(s) in revised form: February 9, 2010
- Published electronically: May 27, 2010
- Communicated by: Bryna Kra
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 4373-4385
- MSC (2010): Primary 37B30, 37B10; Secondary 37M99
- DOI: https://doi.org/10.1090/S0002-9939-2010-10434-3
- MathSciNet review: 2680062