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.
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U2 - 10.1007/s00220-010-1120-x
DO - 10.1007/s00220-010-1120-x
M3 - Article
AN - SCOPUS:77957994532
VL - 300
SP - 411
EP - 433
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 2
ER -