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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Minimal entropy for endomorphisms of the circle
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by Ryuichi Ito PDF
Proc. Amer. Math. Soc. 86 (1982), 321-327 Request permission

Abstract:

Let $f$ be an endomorphism (continuous map) of the circle which has two periodic points of period $m$ and $n$ respectively such that $m \geqslant 2,n \geqslant 2$ and $(m,n) = 1$, then topological entropy $h(f) \geqslant \log {\mu _{m,n}}$ where ${\mu _{m,n}}$ is the largest zero of the polynomial ${x^{m + n}} - {x^m} - {x^n} - 1$.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • 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