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Title: Planar Radial Weakly-Dissipative Diffeomorphisms
Author: Simó, Careles.
Vieiro Yanes, Arturo
Keywords: Homeomorfismes
Sistemes dinàmics de baixa dimensió
Teoria ergòdica
Low-dimensional dynamical systems
Ergodic theory
Issue Date: 29-Dec-2010
Publisher: American Institute of Physics (AIP)
Abstract: We study the effect of a small dissipative radial perturbation acting on a one parameter family of area preserving diffeomorphisms. This is a specific type of dissipative perturbation. The interest is on the global effect of the dissipation on a fixed domain around an elliptic fixed/periodic point of the family, rather than on the effects around a single resonance. We describe the local/global bifurcations observed in the transition from the conservative to a weakly dissipative case: the location of the resonant islands, the changes in the domains of attraction of the foci inside these islands, how the resonances disappear, etc. The possible $\omega$ -limits are determined in each case. This topological description gives rise to three different dynamical regimes according to the size of dissipative perturbation. Moreover, we determine the conservative limit of the probability of capture in a generic resonance from the interpolating flow approximation, hence assuming no homoclinics in the resonance. As a paradigm of weakly dissipative radial maps, we use a dissipative version of the Hénon map.
Note: Reproducció del document publicat a:
It is part of: Chaos, 2010, vol. 20, p. 1-18
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ISSN: 1054-1500
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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