TY - JOUR

T1 - (Non)Invariance of Dynamical Quantities for Orbit Equivalent Flows

AU - Gelfert, Katrin

AU - Motter, Adilson E.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77957994532&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957994532&partnerID=8YFLogxK

U2 - 10.1007/s00220-010-1120-x

DO - 10.1007/s00220-010-1120-x

M3 - Article

AN - SCOPUS:77957994532

SN - 0010-3616

VL - 300

SP - 411

EP - 433

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -