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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 411-433 |
| Number of pages | 23 |
| Journal | Communications in Mathematical Physics |
| Volume | 300 |
| Issue number | 2 |
| DOIs | |
| State | Published - Sep 6 2010 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
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Gelfert, K., & Motter, A. E. (2010). (Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows. Communications in Mathematical Physics, 300(2), 411-433. https://doi.org/10.1007/s00220-010-1120-x