Shadowing by computable chaotic orbits

Julian I. Palmore, Joseph L. McCauley

Research output: Contribution to journalArticlepeer-review

Abstract

We report new results on the shadowing of computable nonperiodic pseudo-orbits by computable chaotic orbits. While ordinary machine truncation/roundoff decisions can produce only periodic pseudo-orbits, we show how nonperiodic pseudo-orbits of chaotic maps can be generated by using for the truncation decision an algorithm for a computable irrational number. The resulting nonperiodic pseudo-orbits are shadowed by unique chaotic orbits of the dynamical system. We illustrate this by constructing examples of nonperiodic pseudo-orbits along with their unique chaotic shadowing orbits for a hyperbolic system. We conclude that the β-shadowing lemma without additional hypotheses provides no information for inferring chaotic attractor statistics from pseudo-orbit statistics in computation.

Original languageEnglish (US)
Pages (from-to)399-402
Number of pages4
JournalPhysics Letters A
Volume122
Issue number8
DOIs
StatePublished - Jun 29 1987

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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