Topological scaling and gap filling at crisis

Scaling laws associated with an interior crisis of chaotic dynamical systems are studied. We argue that open gaps of the chaotic set become densely filled at the crisis due to the sudden appearance of unstable periodic orbits with extremely long periods. We formulate a scaling theory for the associa...

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Bibliographic Details
Published in:Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000-05, Vol.61 (5A), p.5019-5032
Main Authors: Szabo, KG, Lai, YC, Tel, T, Grebogi, C
Format: Article
Language:English
Subjects:
ATTRACTORS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DYNAMICS
ENTROPY
PHASE SPACE
SCALING LAWS
THEORETICAL DATA
TOPOLOGY
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Summary:Scaling laws associated with an interior crisis of chaotic dynamical systems are studied. We argue that open gaps of the chaotic set become densely filled at the crisis due to the sudden appearance of unstable periodic orbits with extremely long periods. We formulate a scaling theory for the associated growth of the topological entropy.
ISSN:1063-651X
1095-3787
DOI:10.1103/PhysRevE.61.5019