Structure of index sequences for mappings with an asymptotic derivative

Alexei Pokrovskii; Oleg Rasskazov

doi:10.3934/dcds.2007.17.653

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2007, Volume 17, Issue 3: 653-670. Doi: 10.3934/dcds.2007.17.653

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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

Received: January 31, 2006

Revised: June 30, 2006

Published: August 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F14; Secondary 58F22.

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