Period doubling and the Lefschetz formula

Author:
John Franks

Journal:
Trans. Amer. Math. Soc. **287** (1985), 275-283

MSC:
Primary 58F20; Secondary 55M20

DOI:
https://doi.org/10.1090/S0002-9947-1985-0766219-1

MathSciNet review:
766219

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Abstract: This article gives an application of the Lefschetz fixed point theorem to prove, under certain hypotheses, the existence of a family of periodic orbits for a smooth map. The family has points of periods for some and all . There is a version of the result for a parametrized family which shows that these orbits are "connected" in parametrized space under appropriate hypotheses.

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DOI:
https://doi.org/10.1090/S0002-9947-1985-0766219-1

Article copyright:
© Copyright 1985
American Mathematical Society