Renyi dimensions from local expansion rates

Year: 1987

Authors: Badii R., Politi A.

Autors Affiliation: Institut für Theoretische Physik, Universität Zürich, Schönberggasse 9, CH-8001 Zurich, Switzerland;
IBM Zurich Research Laboratory, Säumerstrasse 4, CH-8803 Rüschlikon, Switzerland;
Istituto Nazionale di Ottica, Largo E. Fermi 6, 50125 Firenze, Italy

Abstract: A general self-similarity relation is shown to exist, expressing the Renyi-dimension function in terms of local expansion rates both for flows and maps. For the particular case of the information dimension, such an implicit equation yields the well-known Kaplan-Yorke relation. Moreover, it can be explicitly solved in some interesting cases, among which are two-dimensional maps with constant Jacobian. Detailed measurements are performed for the Hénon attractor, with a very accurate estimate of its capacity. Finally, an expansion around the information dimension allows recovery of the Grassberger-Procaccia estimates in an easy way.

Journal/Review: PHYSICAL REVIEW A

Volume: 35 (3)      Pages from: 1288  to: 1293

KeyWords: Renyi dimension function
DOI: 10.1103/PhysRevA.35.1288

Citations: 85
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