Communications in Mathematical Physics

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

(Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows



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.


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© Springer-Verlag 2010

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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