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Morse-Smale endomorphisms of the circle


Author: Louis Block
Journal: Proc. Amer. Math. Soc. 48 (1975), 457-463
MSC: Primary 58F20; Secondary 58F15
DOI: https://doi.org/10.1090/S0002-9939-1975-0413186-5
MathSciNet review: 0413186
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Abstract | References | Similar Articles | Additional Information

Abstract: The orbit structure of a continuously differentiable map $ f$ of the circle is examined, in the case where the nonwandering set of $ f$ is finite and hyperbolic. It is shown that there is a natural number $ n(f)$ such that the period of any periodic point of $ f$ is $ n(f)$ times a power of 2.


References [Enhancements On Off] (What's this?)

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  • [3] M. V. Jakobson, On smooth mappings of the circle into itself, Mat. Sb. 85 (127) (1971), 163-185 = Math. USSR Sb. 14 (1971), 161-185. MR 44 #7587. MR 0290406 (44:7587)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0413186-5
Keywords: Endomorphism, nonwandering set, periodic point
Article copyright: © Copyright 1975 American Mathematical Society

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