Global linearization of periodic difference equations

Anna Cima; Armengol Gasull; Francesc Mañosas

doi:10.3934/dcds.2012.32.1575

Article Contents

2012, Volume 32, Issue 5: 1575-1595. Doi: 10.3934/dcds.2012.32.1575

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Global linearization of periodic difference equations

1.
Dept. de Matemàtiques, Universitat Autònoma de Barcelona, Ediﬁci C, 08193 Bellaterra, Barcelona
2.
Dept. de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, 08193 Bellaterra, Barcelona

Received: October 31, 2010

Revised: February 28, 2011

Published: April 2012

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Abstract

We deal with $m$-periodic, $n$-th order difference equations and study whether they can be globally linearized. We give an affirmative answer when $m=n+1$ and for most of the known examples appearing in the literature. Our main tool is a refinement of the Montgomery-Bochner Theorem.

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Mathematics Subject Classification: Primary: 39A05; Secondary: 39A20, 39B12.

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