Subshifts of finite type in linked twist mappings
Author:
Robert L. Devaney
Journal:
Proc. Amer. Math. Soc. 71 (1978), 334338
MSC:
Primary 58F15
MathSciNet review:
0494289
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Abstract: For each pair of nonzero integers j, k, we define a homeomorphism of the twodisk minus three holes. We show that there exists a compact, invariant, hyperbolic set for each on which is conjugate to a subshift of finite type. This implies that the topological entropy of is bounded below by .
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 J. Franks, Constructing structurally stable diffeomorphisms, Ann. of Math. (2) 105 (1977), 343359. MR 0448434 (56:6740)
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 A. Manning, Topological entropy and the first homology group, Lecture Notes in Math., No. 468, SpringerVerlag, New York, 1975, pp. 185190. MR 0650661 (58:31266)
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 J. Moser, Stable and random motions in dynamical systems, Ann. of Math. Studies, No. 77, Princeton Univ. Press, Princeton, N. J., 1973. MR 0442980 (56:1355)
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 S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747817. MR 0228014 (37:3598)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197804942899
PII:
S 00029939(1978)04942899
Keywords:
Subshift of finite type,
twist mapping,
topological entropy
Article copyright:
© Copyright 1978 American Mathematical Society
