Universal behavior in the parametric evolution of chaotic saddles

Ying Cheng Lai, Karol Życzkowski, Celso Grebogi

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)5261-5265
Number of pages5
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume59
Issue number5
DOIs
StatePublished - 1999
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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