Morse-Smale endomorphisms of the circle
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- by Louis Block
- Proc. Amer. Math. Soc. 48 (1975), 457-463
- DOI: https://doi.org/10.1090/S0002-9939-1975-0413186-5
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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
- L. Block, Bifurcations on endomorphisms of ${S^1}$, Thesis, Northwestern University, Evanston, Ill., 1973.
- Louis Block and John Franke, A classification of the structurally stable contracting endomorphisms of $S^{1}$, Proc. Amer. Math. Soc. 36 (1972), 597โ602. MR 309154, DOI 10.1090/S0002-9939-1972-0309154-1
- M. V. Jakobson, Smooth mappings of the circle into itself, Mat. Sb. (N.S.) 85 (127) (1971), 163โ188 (Russian). MR 0290406
- M. M. Peixoto, Structural stability on two-dimensional manifolds, Topology 1 (1962), 101โ120. MR 142859, DOI 10.1016/0040-9383(65)90018-2
- Michael Shub, Endomorphisms of compact differentiable manifolds, Amer. J. Math. 91 (1969), 175โ199. MR 240824, DOI 10.2307/2373276
- S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747โ817. MR 228014, DOI 10.1090/S0002-9904-1967-11798-1
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- 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