On the prevalence of horseshoes

Young, Lai Sang

doi:10.1090/S0002-9947-1981-0590412-0

On the prevalence of horseshoes
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Trans. Amer. Math. Soc. 263 (1981), 75-88 Request permission

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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