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Title: | Invariant manifolds of dynamical systems close to a rotation: Transverse to the rotation axis | Authors: | BONCKAERT, Patrick Fontich, E |
Issue Date: | 2005 | Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Source: | JOURNAL OF DIFFERENTIAL EQUATIONS, 214(1). p. 128-155 | Abstract: | We consider one parameter families of vector fields depending on a parameter E such that for epsilon = 0 the system becomes a rotation of R-2 x R-n around {0} x R-n and such that for epsilon > 0 the origin is a hyperbolic singular point of saddle type with, say, attraction in the rotation plane and expansion in the complementary space. We look for a local subcenter invariant manifold extending the stable manifolds to epsilon = 0. Afterwards the analogous case for maps is considered. In contrast with the previous case the arithmetic properties of the angle of rotation play an important role. (c) 2005 Elsevier Inc. All rights reserved. | Notes: | Univ Barcelona, Dept Matemat Aplicada & Anal, E-08007 Barcelona, Spain. Limburgs Univ Centrum, B-3590 Diepenbeek, Belgium.Fontich, E, Univ Barcelona, Dept Matemat Aplicada & Anal, Gran Via Corts Catalanes,585, E-08007 Barcelona, Spain.fontich@mat.ub.es | Keywords: | perturbations of rotations; subcenter invariant manifolds; bifurcations | Document URI: | http://hdl.handle.net/1942/2081 | ISSN: | 0022-0396 | e-ISSN: | 1090-2732 | DOI: | 10.1016/j.jde.2005.02.012 | ISI #: | 000229861300005 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2006 |
Appears in Collections: | Research publications |
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