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Unstable dimension variability and codimension-one bifurcations of two-dimensional maps

  • Unstable dimension variability is a mechanism whereby an invariant set of a dynamical system, like a chaotic attractor or a strange saddle, loses hyperbolicity in a severe way, with serious consequences on the shadowability properties of numerically generated trajectories. In dynamical systems possessing a variable parameter, this phenomenon can be triggered by the bifurcation of an unstable periodic orbit. This Letter aims at discussing the possible types of codimension-one bifurcations leading to unstable dimension variability in a two-dimensional map, presenting illustrative examples and displaying numerical evidences of this fact by computing finite-time Lyapunov exponents. (C) 2004 Elsevier B.V. All rights reserved

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Author:Ricardo L. Viana, José R. R. Barbosa, Celso Grebogi
Document Type:Article
Year of first Publication:2004
Year of Completion:2004
Release Date:2017/03/24
Source:Physics Letters / A. - ISSN 0375-9601. - 321 (2004), 4, S. 244 - 251
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie
Peer Review:Referiert
Publication Way:Open Access
Institution name at the time of publication:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik