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Title: Topological scaling and gap filling at crisis

Abstract

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. (c) 2000 The American Physical Society.

Authors:
 [1];  [2];  [3];  [4];  [5]
  1. Department of Mathematics, University of Kansas, Lawrence, Kansas 66045 (United States)
  2. (Hungary)
  3. Department of Mathematics and Department of Electrical Engineering, Arizona State University, Tempe, Arizona 85287 (United States)
  4. Institute for Theoretical Physics, Eoetvoes University, P.O. Box 32, Budapest, H-1518, (Hungary)
  5. Institute for Plasma Research, Department of Mathematics, and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)
Publication Date:
OSTI Identifier:
20216390
Resource Type:
Journal Article
Journal Name:
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Additional Journal Information:
Journal Volume: 61; Journal Issue: 5; Other Information: PBD: May 2000; Journal ID: ISSN 1063-651X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DYNAMICS; SCALING LAWS; TOPOLOGY; PHASE SPACE; ENTROPY; ATTRACTORS; THEORETICAL DATA

Citation Formats

Szabo, K. Gabor, Institute for Theoretical Physics, Eoetvoes University, P.O. Box 32, Budapest, H-1518,, Lai, Ying-Cheng, Tel, Tamas, and Grebogi, Celso. Topological scaling and gap filling at crisis. United States: N. p., 2000. Web. doi:10.1103/PhysRevE.61.5019.
Szabo, K. Gabor, Institute for Theoretical Physics, Eoetvoes University, P.O. Box 32, Budapest, H-1518,, Lai, Ying-Cheng, Tel, Tamas, & Grebogi, Celso. Topological scaling and gap filling at crisis. United States. doi:10.1103/PhysRevE.61.5019.
Szabo, K. Gabor, Institute for Theoretical Physics, Eoetvoes University, P.O. Box 32, Budapest, H-1518,, Lai, Ying-Cheng, Tel, Tamas, and Grebogi, Celso. Mon . "Topological scaling and gap filling at crisis". United States. doi:10.1103/PhysRevE.61.5019.
@article{osti_20216390,
title = {Topological scaling and gap filling at crisis},
author = {Szabo, K. Gabor and Institute for Theoretical Physics, Eoetvoes University, P.O. Box 32, Budapest, H-1518, and Lai, Ying-Cheng and Tel, Tamas and Grebogi, Celso},
abstractNote = {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. (c) 2000 The American Physical Society.},
doi = {10.1103/PhysRevE.61.5019},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
issn = {1063-651X},
number = 5,
volume = 61,
place = {United States},
year = {2000},
month = {5}
}