Communications in Mathematical Physics

, Volume 300, Issue 2, pp 411–433 | Cite as

(Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows

  • Katrin GelfertEmail author
  • Adilson E. Motter


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.


Lyapunov Exponent Hausdorff Dimension Topological Entropy Borel Probability Measure Time Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Authors and Affiliations

  1. 1.Instituto de MatemáticaUFRJ, Cidade Universitária - Ilha do FundãoRio de JaneiroBrazil
  2. 2.Department of Physics and Astronomy & Northwestern Institute on Complex SystemsNorthwestern UniversityEvanstonUSA

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