Subshifts of finite type in linked twist mappings

Devaney, Robert L.

doi:10.1090/S0002-9939-1978-0494289-9

Subshifts of finite type in linked twist mappings
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by Robert L. Devaney PDF

Proc. Amer. Math. Soc. 71 (1978), 334-338 Request permission

Abstract:

For each pair of nonzero integers j, k, we define a homeomorphism ${f_{j,k}}$ of the two-disk minus three holes. We show that there exists a compact, invariant, hyperbolic set for each ${f_{j,k}}$ on which ${f_{j,k}}$ is conjugate to a subshift of finite type. This implies that the topological entropy of ${f_{j,k}}$ is bounded below by $4|j||k| - 2|j| - 2|k|$.

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