ISSN:
1089-7682
Source:
AIP Digital Archive
Topics:
Physics
Notes:
We consider a dynamical system with state space M, a smooth, compact subset of some Rn, and evolution given by Tt, xt=Ttx, x∈M; Tt is invertible and the time t may be discrete, t∈Z, Tt=Tt, or continuous, t∈R. Here we show that starting with a continuous positive initial probability density ρ(x,0)〉0, with respect to dx, the smooth volume measure induced on M by Lebesgue measure on Rn, the expectation value of logρ(x,t), with respect to any stationary (i.e., time invariant) measure ν(dx), is linear in t, ν(logρ(x,t))=ν(logρ(x,0))+Kt. K depends only on ν and vanishes when ν is absolutely continuous with respect to dx.© 1998 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.166321
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