Characterization of transition to chaos with multiple positive - Lyapunov exponents by unstable periodic orbits

R Davidchack, Y C Lai, Ying-Cheng Lai

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

We investigate how the transition to chaos with multiple positive Lyapunov exponents can be characterized by the set of infinite number of unstable periodic orbits embedded in the chaotic invariant set. We argue and provide numerical confirmation that the transition is generally accompanied by a nonhyperbolic behavior: unstable dimension variability. As a consequence, the Lyapunov exponents, except for the largest one, pass through zero continuously. (C) 2000 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)308-313
Number of pages6
JournalPhysics Letters A
Volume270
Issue number6
Publication statusPublished - 12 Jun 2000

Keywords

  • HIGH-DIMENSIONAL CHAOS
  • FRACTAL DIMENSION
  • DYNAMICAL-SYSTEMS
  • RING CAVITY
  • ATTRACTORS
  • VARIABILITY
  • TURBULENCE
  • CRISES
  • SPACE

Cite this