(Non)Invariance of dynamical quantities for orbit equivalent flows

Details (Non)Invariance of dynamical quantities for orbit equivalent flows (Non)Invariance of dynamical quantities for orbit equivalent flows

2010-10-08

arxiv.org/abs/1010.1791v1

Commun.Math.Phys.300:411-433,2010

Mathematics

Dynamical Systems

Scientific paper

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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