Period doubling and the lefschetz formula

John M Franks

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

Period doubling and the lefschetz formula

John M Franks^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

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^kp for some p and all k > 0. There is a version of the result for a parametrized family ft which shows that these orbits are “connected” in parametrized space under appropriate hypotheses.

Original language	English (US)
Pages (from-to)	275-283
Number of pages	9
Journal	Transactions of the American Mathematical Society
Volume	287
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9947-1985-0766219-1
State	Published - Jan 1 1985

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9947-1985-0766219-1

Cite this

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AB - 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 2kp for some p and all k > 0. There is a version of the result for a parametrized family ft which shows that these orbits are “connected” in parametrized space under appropriate hypotheses.

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Period doubling and the lefschetz formula

Abstract

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