On dynamical systems close to a product of $m$ rotations

Patrick Bonckaert; Timoteo Carletti; Ernest Fontich

doi:10.3934/dcds.2009.24.349

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2009, Volume 24, Issue 2: 349-366. Doi: 10.3934/dcds.2009.24.349

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On dynamical systems close to a product of $m$ rotations

1.
Hasselt University, Agoralaan, gebouw D, B-3590 Diepenbeek
2.
Department of Mathematics FUNDP, Rempart de la Vierge, 8, B-5000 Namur
3.
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona

Received: April 30, 2007

Revised: May 31, 2008

Published: May 2009

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Abstract

We consider one parameter families of analytic vector fields and diffeomorphisms, including for a parameter value, say $\varepsilon = 0$, the product of rotations in $\R^{2m}\times \R^n$ such that for positive values of the parameter the origin is a hyperbolic point of saddle type. We address the question of determining the limit stable invariant manifold when $\varepsilon$ goes to zero as a subcenter invariant manifold when $\varepsilon = 0$.

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Mathematics Subject Classification: Primary: 37D10; Secondary: 34E10, 37G10.

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