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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Symbolic dynamics for nonhyperbolic systems


Authors: David Richeson and Jim Wiseman
Journal: Proc. Amer. Math. Soc. 138 (2010), 4373-4385
MSC (2010): Primary 37B30, 37B10; Secondary 37M99
Published electronically: May 27, 2010
MathSciNet review: 2680062
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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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Additional Information

David Richeson
Affiliation: Department of Mathematics and Computer Science, Dickinson College, Carlisle, Pennsylvania 17013
Email: richesod@dickinson.edu

Jim Wiseman
Affiliation: Department of Mathematics, Agnes Scott College, Decatur, Georgia 30030
Email: jwiseman@agnesscott.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10434-3
PII: S 0002-9939(2010)10434-3
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.