On the prevalence of horseshoes
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- by Lai Sang Young
- Trans. Amer. Math. Soc. 263 (1981), 75-88
- DOI: https://doi.org/10.1090/S0002-9947-1981-0590412-0
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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.References
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Bibliographic Information
- © Copyright 1981 American Mathematical Society
- 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