(Non)Invariance of dynamical quantities for orbit equivalent flows
Dynamical Systems
2011-03-07 v1 General Relativity and Quantum Cosmology
Chaotic Dynamics
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.
Cite
@article{arxiv.1010.1791,
title = {(Non)Invariance of dynamical quantities for orbit equivalent flows},
author = {Katrin Gelfert and Adilson E. Motter},
journal= {arXiv preprint arXiv:1010.1791},
year = {2011}
}