Physical Review E. Statistical, Nonlinear, and Soft Matter Physics (Phys. Rev. E (3)) (19950101), 51, no.~3, part A, 1989-1995. ISSN: 1539-3755 (print).eISSN: 1550-2376.
Subject
58 Global analysis, analysis on manifolds -- 58F Ordinary differential equations on manifolds; dynamical systems 58F13 Strange attractors; chaos and other pathologies
Language
English
Online Access
초록
The curve of the topological entropy of the logistic map of the interval versus the parameter value is studied from the point of view of its fractal properties. Generalized dimensions, singularity spectra, and ``thermodynamic functions'' are computed numerically (with more than 1000 CPU hours on a VAX 8350). Slight disagreement is found between the Gibbs ensemble method (here referred to as the ``Halsey method'') and the canonical one (referred to as ``Chhabra-Jensen's'').