Scaling laws for invariant measures on hyperbolic and nonhyperbolic attractors
Anno: 1988
Autori: Grassberger P., Badii R., Politi A.
Affiliazione autori: Physics Department, University of Wuppertal, D-5600 Wuppertal 1, Federal Republic of Germany;
Institute of Theoretical Physics, University of Zurich, CH-8001 Zurich, Switzerland;
Istituto Nazionale di Ottica, Largo E. Fermi 6, I-50125 Firenze, Italy
Abstract: The analysis of dynamical systems in terms of spectra of singularities is extended to higher dimensions and to nonhyperbolic systems. Prominent roles in our approach are played by the generalized partial dimensions of the invariant measure and by the distribution of effective Liapunov exponents. For hyperbolic attractors, the latter determines the metric entropies and provides one constraint on the partial dimensions. For nonhyperbolic attractors, there are important modifications. We discuss them for the examples of the logistic and Hénon map. We show, in particular, that the generalized dimensions have singularities with noncontinuous derivative, similar to first-order phase transitions in statistical mechanics.
Giornale/Rivista: JOURNAL OF STATISTICAL PHYSICS
Volume: 51 (1/2) Da Pagina: 135 A: 179
Parole chiavi: Dynamical systems; generalized dimensions and entropies; DOI: 10.1007/BF01015324Citazioni: 417dati da “WEB OF SCIENCE” (of Thomson Reuters) aggiornati al: 2024-05-12Riferimenti tratti da Isi Web of Knowledge: (solo abbonati) Link per visualizzare la scheda su IsiWeb: Clicca quiLink per visualizzare la citazioni su IsiWeb: Clicca qui