Devil-staircase behavior of dynamical invariants in chaotic scattering

K Zyczkowski, Y C Lai, Ying-Cheng Lai

Research output: Contribution to journalArticlepeer-review

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. (C) 2000 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)197-216
Number of pages20
JournalPhysica. D, Nonlinear Phenomena
Volume142
Issue number3-4
Publication statusPublished - 15 Aug 2000

Keywords

  • chaotic scattering
  • dynamical invariants
  • devil staircase
  • LEAPFROGGING VORTEX PAIRS
  • OPEN HYDRODYNAMICAL FLOWS
  • STRANGE ATTRACTORS
  • GENERALIZED DIMENSIONS
  • TOPOLOGICAL-ENTROPY
  • SYMBOLIC DYNAMICS
  • PERIODIC-ORBITS
  • CHEMICAL CHAOS
  • COMMUNICATION
  • SADDLES

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