(Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows

Katrin Gelfert*, Adilson E. Motter

*Corresponding author for this work

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

We study how dynamical quantities such as Lyapunov exponents, metric entropy, topological pressure, recurrence rates, and dimension-like characteristics change under a time reparameterization of a dynamical system. These quantities are shown to either remain invariant, transform according to a multiplicative factor or transform through a convoluted dependence that may take the form of an integral over the initial local values. We discuss the significance of these results for the apparent non-invariance of chaos in general relativity and explore applications to the synchronization of equilibrium states and the elimination of expansions.

Original languageEnglish (US)
Pages (from-to)411-433
Number of pages23
JournalCommunications in Mathematical Physics
Volume300
Issue number2
DOIs
StatePublished - Sep 6 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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