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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Subshifts of finite type in linked twist mappings


Author: Robert L. Devaney
Journal: Proc. Amer. Math. Soc. 71 (1978), 334-338
MSC: Primary 58F15
MathSciNet review: 0494289
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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\vert j\vert\vert k\vert - 2\vert j\vert - 2\vert k\vert$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0494289-9
PII: S 0002-9939(1978)0494289-9
Keywords: Subshift of finite type, twist mapping, topological entropy
Article copyright: © Copyright 1978 American Mathematical Society