Universal behavior in the parametric evolution of chaotic saddles

Journal Article · Sat May 01 04:00:00 EDT 1999 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.59.5261· OSTI ID:338688

Lai, Y ^[1]; Zyczkowski, K; Grebogi, C ^[2]; Zyczkowski, K ^[3]; Grebogi, C ^[4]

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1. Department of Physics and Astronomy and Department of Mathematics, University of Kansas, Lawrence, Kansas 66045 (United States)
2. Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States)
3. Instytut Fizyki im. Smoluchowskiego, Uniwersytet Hagiellonski, ulica Reymonta 4, 30-059 Krakow (Poland)
4. Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)

Chaotic saddles are nonattracting dynamical invariant sets that physically lead to transient chaos. As a system parameter changes, chaotic saddles can evolve via an infinite number of homoclinic or heteroclinic tangencies of their stable and unstable manifolds. Based on previous numerical evidence and a rigorous analysis of a class of representative models, we show that dynamical invariants such as the topological entropy and the fractal dimension of chaotic saddles obey a universal behavior: they exhibit a devil-staircase characteristic as a function of the system parameter. {copyright} {ital 1999} {ital The American Physical Society}

• OSTI ID: 338688
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 5 Vol. 59; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CLASSICAL MECHANICS
DYNAMICS
ENTROPY
PHASE SPACE
TOPOLOGY