Symbolic dynamics for nonhyperbolic systems
نویسندگان
چکیده
منابع مشابه
Symbolic Dynamics for Nonhyperbolic Systems
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 possess...
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◦ Geodesic flows on compact manifolds with negative sectional curvature. Later, we relax uniform hyperbolicity to an asymptotic one, called non-uniform hyperbolicity. Two examples of such systems are: ◦ Slow down of fA : T → T, see [9]. ◦ Geodesic flows on surfaces with nonpositive curvature. Introductory example: Smale’s horseshoe [21]. Let g : K → K be Smale’s horseshoe map, and σ : Σ→ Σ the ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2010
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-2010-10434-3