Periodic orbits and the continuity of rotation numbers
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- by Richard Swanson PDF
- Proc. Amer. Math. Soc. 117 (1993), 269-273 Request permission
Abstract:
The main result is that an annulus homeomorphism homotopic to the identity either has a well-defined and continuous assignment of rotation numbers on its chain recurrent set or there exists an interval of rotation numbers and periodic points corresponding to each reduced rational number in the interval. As a corollary, rotational discontinuities force the mapping to admit periodic points of all sufficiently large periods $n$. In a related result, we provide a criterion for the rotation set of an annulus homeomorphism to be nowhere dense.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 269-273
- MSC: Primary 58F20; Secondary 54H20
- DOI: https://doi.org/10.1090/S0002-9939-1993-1112502-X
- MathSciNet review: 1112502