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 (3)      Pages from: 263  to: 286

KeyWords: hyperbolic dynamical systems
DOI: 10.1016/0167-2789(89)90085-7

Citations: 12
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