(Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows |
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Authors: | Katrin Gelfert Adilson E Motter |
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Institution: | 1. Instituto de Matemática, UFRJ, Cidade Universitária - Ilha do Fund?o, Rio de Janeiro, 21945-909, Brazil 2. Department of Physics and Astronomy & Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois, 60208-3112, USA
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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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Keywords: | |
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