Communications in Mathematical Physics

, Volume 300, Issue 2, pp 411–433

(Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows


    • Instituto de MatemáticaUFRJ, Cidade Universitária - Ilha do Fundão
  • Adilson E. Motter
    • Department of Physics and Astronomy & Northwestern Institute on Complex SystemsNorthwestern University

DOI: 10.1007/s00220-010-1120-x

Cite this article as:
Gelfert, K. & Motter, A.E. Commun. Math. Phys. (2010) 300: 411. doi:10.1007/s00220-010-1120-x


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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