Time-metric equivalence and dimension change under time reparameterizations

Adilson E. Motter, Katrin Gelfert

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We study the behavior of dynamical systems under time reparameterizations, which is important not only to characterize chaos in relativistic systems but also to probe the invariance of dynamical quantities. We first show that time transformations are locally equivalent to metric transformations, a result that leads to a transformation rule for all Lyapunov exponents on arbitrary Riemannian phase spaces. We then show that time transformations preserve the spectrum of generalized dimensions Dq except for the information dimension D1, which, interestingly, transforms in a nontrivial way despite previous assertions of invariance. The discontinuous behavior at q=1 can be used to constrain and extend the formulation of the Kaplan-Yorke conjecture.

Original languageEnglish (US)
Article number065202
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number6
StatePublished - Jun 9 2009

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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