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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 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dynamical Systems: An International Journal Taylor & Francis

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

14 pages

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References (23)

Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1468-9375
eISSN
1468-9367
DOI
10.1080/14689360802413929
Publisher site
See Article on Publisher Site

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.

Journal

Dynamical Systems: An International JournalTaylor & Francis

Published: Dec 1, 2008

Keywords: fixed point index; periodic points; iterations; C 1 maps; Primary 37C25; Secondary 37C05

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