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August  2007, 17(3): 653-670. doi: 10.3934/dcds.2007.17.653

Structure of index sequences for mappings with an asymptotic derivative

Alexei Pokrovskii 1, and  Oleg Rasskazov 1,

1. 

Department of Applied Mathematics, University College, Cork, Ireland, Ireland

Received  February 2006 Revised  July 2006 Published  December 2006

Properties of the sequence ind$(\infty,\id-f^{m}),$ $m=1,2,\ldots$ where $f^{m}$ is the $m$-th iterate of the mapping $ f:R^{d}\to R^{d}$, and ind denotes the Kronecker index are investigated. The case when $f$ has the asymptotic derivative $A$ at infinity and some eigenvalues of $A$ are roots of unity is of primary interest.
Keywords: Index sequence, topological degree, index at infinity..
Mathematics Subject Classification: Primary: 58F14; Secondary 58F2.
Citation: Alexei Pokrovskii, Oleg Rasskazov. Structure of index sequences for mappings with an asymptotic derivative. Discrete & Continuous Dynamical Systems, 2007, 17 (3) : 653-670. doi: 10.3934/dcds.2007.17.653
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