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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the prevalence of horseshoes


Author: Lai Sang Young
Journal: Trans. Amer. Math. Soc. 263 (1981), 75-88
MSC: Primary 58F15; Secondary 28D20
DOI: https://doi.org/10.1090/S0002-9947-1981-0590412-0
MathSciNet review: 590412
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Abstract: In this paper the symbolic dynamics of several differentiable systems are investigated. It is shown that many well-known dynamical systems, including Axiom $ {\text{A}}$ systems, piecewise monotonic maps of the interval, the Lorenz attractor and Abraham-Smale examples, have inside them subsystems conjugate to subshifts of finite type. These subsystems have hyperbolic structures and hence are stable. They can also be chosen to have entropy arbitrarily close to that of the ambient system.


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DOI: https://doi.org/10.1090/S0002-9947-1981-0590412-0
Keywords: Subshift of finite type, topological entropy, hyperbolicity
Article copyright: © Copyright 1981 American Mathematical Society