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Proceedings of the American Mathematical Society

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

 

 

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: 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

DOI: https://doi.org/10.1090/S0002-9939-1982-0667298-5
Keywords: $ A$-graph, loop, periodic point, rotation set, topological entropy
Article copyright: © Copyright 1982 American Mathematical Society