Period doubling and the Lefschetz formula

Franks, John

doi:10.1090/S0002-9947-1985-0766219-1

Period doubling and the Lefschetz formula
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by John Franks

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

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

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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 ${2^k}p$ for some $p$ and all $k \geq 0$. There is a version of the result for a parametrized family $f_t$ which shows that these orbits are "connected" in parametrized space under appropriate hypotheses.

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