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Phys. Rev. E 59, 5261 - 5265 (1999)

Universal behavior in the parametric evolution of chaotic saddles

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Ying-Cheng Lai1, Karol Życzkowski2,3, and Celso Grebogi2,4
1Department of Physics and Astronomy and Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
2Institute for Plasma Research, University of Maryland, College Park, Maryland 20742
3Instytut Fizyki im. Smoluchowskiego, Uniwersytet Hagielloński, ulica Reymonta 4, 30-059 Kraków, Poland
4Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742

Received 8 October 1998; revised 13 January 1999

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.


©1999 The American Physical Society

URL: http://link.aps.org/abstract/PRE/v59/p5261
DOI: 10.1103/PhysRevE.59.5261
PACS: 05.45.-a

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