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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Period doubling and the Lefschetz formula


Author: John Franks
Journal: Trans. Amer. Math. Soc. 287 (1985), 275-283
MSC: Primary 58F20; Secondary 55M20
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 $ {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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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0766219-1
PII: S 0002-9947(1985)0766219-1
Article copyright: © Copyright 1985 American Mathematical Society