(Non)Invariance of dynamical quantities for orbit equivalent flows
arXiv:1010.1791 · doi:10.1007/s00220-010-1120-x
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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- Free motion around black holes with discs or rings: between integrability and chaos - III
- Adjusting chaotic indicators to curved spacetimes
- Strong symbolic dynamics for geodesic flow on CAT(-1) spaces and other metric Anosov flows
- Non-affine geometrization can lead to nonphysical instabilities
- Time change for flows and thermodynamic formalism