# American Institute of Mathematical Sciences

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

## Structure of index sequences for mappings with an asymptotic derivative

 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.
Citation: Alexei Pokrovskii, Oleg Rasskazov. Structure of index sequences for mappings with an asymptotic derivative. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 653-670. doi: 10.3934/dcds.2007.17.653
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