Towards complete detection of unstable periodic orbits in chaotic systems

Ruslan L. Davidchack, Ying-Cheng Lai, Aaron Klebanoff, Erik M. Bollt

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


We present a rigorous analysis and numerical evidence indicating that a recently developed methodology for detecting unstable periodic orbits is capable of yielding all orbits up to periods limited only by the computer precision. In particular, we argue that an efficient convergence to every periodic orbit can be achieved and the basin of attraction can be made finite and accessible for typical or particularly chosen initial conditions. (C) 2001 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)99-104
Number of pages6
JournalPhysics Letters A
Issue number1-2
Publication statusPublished - 20 Aug 2001


  • dynamical-systems
  • strange attractor
  • ring cavity
  • map


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