Systematic Computation of the Least Unstable Periodic Orbits in Chaotic Attractors

Fotis K. Diakonos, Peter Schmelcher, Ofer Biham

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

We show that a recently proposed numerical technique for the calculation of unstable periodic orbits in chaotic attractors is capable of finding the least unstable periodic orbits of any given order. This is achieved by introducing a modified dynamical system which has the same set of periodic orbits as the original chaotic system, but with a tuning parameter which is used to stabilize the orbits selectively. This technique is central for calculations using the stability criterion for the truncation of cycle expansions, which provide highly improved convergence of calculations of dynamical averages in generic chaotic attractors. The approach is demonstrated for the Hénon attractor.

Original languageAmerican English
Pages (from-to)4349-4352
Number of pages4
JournalPhysical Review Letters
Volume81
Issue number20
DOIs
StatePublished - 16 Nov 1998

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