Dimension function and phase transition-like behavior in strange attractors
Year: 1987
Authors: Badii R., Politi A.
Autors Affiliation: Institut f�r Theoretische Physik, Sch�nberggasse 9, 8001 Zurich, Switzerland
IBM Research Division, Zurich Research Laboratory, S�umerstrasse 4, 8803 R�schlikon, Switzerland
Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy
Abstract: Recently introduced conservation laws for volume expansion rates are used as a tool to investigate changes in the geometric and dynamical structure of strange attractors occurring, e.g., upon variation of a parameter. The appearance of edges in the Renyi dimension function Dq and metric entropy Kq is an indication of such transitions. A way to classify them by introducing two new indices jq and jq+ is discussed. Moreover, these critical points can be analyzed in terms of phase transitions, in the framework of the thermodynamic formalism for dynamical systems.
Journal/Review: PHYSICA SCRIPTA
Volume: 35 Pages from: 243 to: 246
KeyWords: dynamical systems
DOI: 10.1088/0031-8949/35/3/005
Citations: 29
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