### 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) |
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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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## Cite this

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