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General form of fixed point indices of an iterated C 1 map and infiniteness of minimal periods

General form of fixed point indices of an iterated C 1 map and infiniteness of minimal periods

Abstract

Let f be a smooth self-map of a compact manifold and be a family of compact subsets of periodic points of f . Under some natural condition on the family we find the form of the sequence of indices of iterations , which generalizes the classical theorem of Chow, Mallet-Paret and Yorke. We apply this knowledge to study the structure of periodic points of f . In particular, we show that a map f with unbounded sequence of Lefschetz numbers of iterations , which satisfies some assumption put on derivatives at periodic points, has an infinite number of minimal periods.
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