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(Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows

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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.

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Authors and Affiliations

  1. Instituto de Matemática, UFRJ, Cidade Universitária - Ilha do Fundão, Rio de Janeiro, 21945-909, Brazil

    Katrin Gelfert

  2. Department of Physics and Astronomy & Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois, 60208-3112, USA

    Adilson E. Motter

Authors
  1. Katrin Gelfert
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  2. Adilson E. Motter
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Correspondence to Katrin Gelfert.

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Communicated by G. Gallavotti

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Gelfert, K., Motter, A.E. (Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows. Commun. Math. Phys. 300, 411–433 (2010). https://doi.org/10.1007/s00220-010-1120-x

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  • DOI: https://doi.org/10.1007/s00220-010-1120-x

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