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
| Author details: | Ricardo L. Viana, José R. R. Barbosa, Celso Grebogi |
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| ISSN: | 0375-9601 |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2004 |
| Publication year: | 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 |
| Publishing method: | Open Access |
| Institution name at the time of the publication: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik |
