Minimal entropy for endomorphisms of the circle
Author:
Ryuichi Ito
Journal:
Proc. Amer. Math. Soc. 86 (1982), 321-327
MSC:
Primary 58F20; Secondary 58F11
DOI:
https://doi.org/10.1090/S0002-9939-1982-0667298-5
MathSciNet review:
667298
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be an endomorphism (continuous map) of the circle which has two periodic points of period
and
respectively such that
and
, then topological entropy
where
is the largest zero of the polynomial
.
- [1] C. Bernhardt, Rotation intervals of endomorphisms of the circle, Ph. D. Thesis, University of Warwick, 1980.
- [2] L. Block, E. M. Coven and Z. Nitecki, Minimizing topological entropy for maps of the circle, preprint. MR 661815 (83h:58058)
- [3] L. Block, J. Guckenheimer, M. Misiurewicz and L. S. Young, Periodic points and topological entropy of one dimensional maps, Global Theory of Dynamical Systems, Proceedings, Northwestern Univ., 1979, Lecture Notes in Math., vol. 819, Springer-Verlag, Berlin and New York, 1980, pp. 18-34. MR 591173 (82j:58097)
- [4] R. Ito, Rotation sets are closed, Math. Proc. Cambridge Philos. Soc. 89 (1981), 107-111. MR 591976 (82i:58061)
- [5] M. Misiurewicz and W. Szlenk, Entropy of piecewise monotone mappings, Studia Math. 67 (1980), 45-63. MR 579440 (82a:58030)
- [6] S. Newhouse, J. Palis and F. Takens, Stable families of dynamical systems. I: Diffeomorphisms, preprint, I.M.P.A., Rio, Brazil.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1982-0667298-5
Keywords:
-graph,
loop,
periodic point,
rotation set,
topological entropy
Article copyright:
© Copyright 1982
American Mathematical Society