A canonical partition of the periodic orbits of chaotic maps

Author:
Kathleen T. Alligood

Journal:
Trans. Amer. Math. Soc. **292** (1985), 713-719

MSC:
Primary 58F12; Secondary 34C35, 58F08, 58F13, 58F22

DOI:
https://doi.org/10.1090/S0002-9947-1985-0808749-X

MathSciNet review:
808749

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Abstract: We show that the periodic orbits of an area-contracting horseshoe map can be partitioned into subsets of orbits of minimum period , for some positive integer . This partition is natural in the following sense: for any parametrized area-contracting map which forms a horseshoe, the orbits in one subset of the partition are contained in a single component of orbits in the full parameter space. Furthermore, prior to the formation of the horseshoe, this component contains attracting orbits of minimum period , for each nonnegative integer .

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DOI:
https://doi.org/10.1090/S0002-9947-1985-0808749-X

Article copyright:
© Copyright 1985
American Mathematical Society