Fixed point indices of iterated smooth maps in arbitrary dimension

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:251

Article

Graff, Grzegorz¹  Jezierski, Jerzy²  Nowak-Przygodzki, Piotr¹ 

[1] Gdansk Univ Technol, Fac Appl Phys & Math, PL-80233 Gdansk, Poland

[2] Warsaw Univ Life Sci SGGW, Inst Applicat Math, PL-00757 Warsaw, Poland

关键词: Fixed point index;    Smooth maps;    Iterations;   

DOI  :  10.1016/j.jde.2011.05.024

来源: Elsevier

【 摘 要 】

Let f be a smooth self-map of R(m), when m is an arbitrary natural number. We give a complete description of possible sequences of indices of iterations of f at an isolated fixed point, answering in affirmative the Chow, Mallet-Paret and Yorke conjecture posed in [S.N. Chow, J. Mallet-Parret, J.A. Yorke, A periodic point index which is a bifurcation invariant, in: Geometric Dynamics, Rio de Janeiro, 1981, in: Lecture Notes in Math., vol. 1007, Springer, Berlin, 1983, pp. 109-131]. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free