Fixed point indices of iterations of $C^1$ maps in $R^3$

Grzegorz Graff; Piotr Nowak-Przygodzki

doi:10.3934/dcds.2006.16.843

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2006, Volume 16, Issue 4: 843-856. Doi: 10.3934/dcds.2006.16.843

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Fixed point indices of iterations of $C^1$ maps in $R^3$

Grzegorz Graff^1, and
Piotr Nowak-Przygodzki^1,

1.
Department of Algebra, Faculty of Applied Physics and Mathematics, Gdansk University of Technology, ul. Narutowicza 11/12, 80-952 Gdansk

Received: September 30, 2005

Revised: July 31, 2006

Published: September 2006

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Abstract

In the case of a $C^1$ self-map of $R^3$ we prove the Chow, Mallet-Paret and Yorke conjecture on the form of sequences of local fixed point indices of iterations and give a complete description of possible sequences of indices.

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Mathematics Subject Classification: Primary: 37C25, Secondary: 37C05.

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