Devil-staircase behavior of dynamical invariants in chaotic scattering

Karol Zyczkowski, Ying-Cheng Lai

Research output: Contribution to journalArticle

Abstract

A crisis in chaotic scattering is characterized by the merging of two or more nonattracting chaotic saddles. The fractal dimension of the resulting chaotic saddle increases through the crisis. We present a rigorous analysis for the behavior of dynamical invariants associated with chaotic scattering by utilizing a representative model system that captures the essential dynamical features of crisis. Our analysis indicates that the fractal dimension and other dynamical invariants are a devil-staircase type of function of the system parameter. Our results can also provide insight for similar devil-staircase behaviors observed in the parametric evolution of chaotic saddles of general dissipative dynamical systems and in communicating with chaos.

Original languageEnglish (US)
Pages (from-to)197-216
Number of pages20
JournalPhysica D: Nonlinear Phenomena
Volume142
Issue number3-4
DOIs
StatePublished - Aug 15 2000

Keywords

  • Chaotic scattering
  • Devil staircase
  • Dynamical invariants

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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