Long-range order in the scaling behaviour of hyperbolic dynamical-systems
Year: 1989
Authors: Paoli P., Politi A., Badii R.
Autors Affiliation: Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy;
Department of Chemical Physics, The Weizmann Institute of Science, IL-76100, Rehovot, Israel
Abstract: Detailed statistical analyses of chaotic signals have been so far limited to 2-d maps with one expanding and one contracting direction. Here, by studying filtered signals, we provide evidence that the existence of a further stable direction can transform self-similarity into self-affinity and generate phase transitions (according to the thermodynamic formalism of dynamical systems). In a hyperbolic case, the dimension spectrum is computed exactly as a function of the filter cut-off frequency. Moreover, the validity of the Kaplan-Yorke formula and of its generalization are rigorously proven. Finally, the scaling function is shown to satisfy a stochastic recursive relation, whose Lyapunov exponent allows to control the extension of the range of interactions in the associated Hamiltonian.
Journal/Review: PHYSICA D-NONLINEAR PHENOMENA
Volume: 36 Pages from: 263 to: 286
KeyWords: hyperbolic dynamical systemsCitations: 13data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-04-28References taken from IsiWeb of Knowledge: (subscribers only)