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June  2009, 24(2): 349-366. doi: 10.3934/dcds.2009.24.349

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

Patrick Bonckaert 1, , Timoteo Carletti 2, and  Ernest Fontich 3,

1. 

Hasselt University, Agoralaan, gebouw D, B-3590 Diepenbeek
2. 

Department of Mathematics FUNDP, Rempart de la Vierge, 8, B-5000 Namur, Belgium
3. 

Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona

Received  May 2007 Revised  June 2008 Published  March 2009

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 $\varepsilon = 0$.
Keywords: subcenter invariant manifolds, bifurcations., Perturbations of rotations.
Mathematics Subject Classification: Primary: 37D10; Secondary: 34E10, 37G1.
Citation: Patrick Bonckaert, Timoteo Carletti, Ernest Fontich. On dynamical systems close to a product of $m$ rotations. Discrete and Continuous Dynamical Systems, 2009, 24 (2) : 349-366. doi: 10.3934/dcds.2009.24.349
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