Universal behavior in the parametric evolution of chaotic saddles

Ying-Cheng Lai, Karol Zyczkowski, Celso Grebogi

Research output: Contribution to journalArticle

14 Citations (Scopus)

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. [S1063-651X(99)01605-0].

Original languageEnglish
Pages (from-to)5261-5265
Number of pages5
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume59
Issue number5
DOIs
Publication statusPublished - 1 May 1999

Keywords

  • leapfrogging vortex pairs
  • open hydrodynamical flows
  • topological-entropy
  • symbolic dynamics
  • chemical chaos
  • attractors
  • scattering
  • communication
  • crisis
  • noise

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