# Remark on the (non)convergence of ensemble densities in dynamical systems.

@article{Goldstein1998RemarkOT, title={Remark on the (non)convergence of ensemble densities in dynamical systems.}, author={Sheldon Goldstein and Joel L Lebowitz and Yakov G. Sinai}, journal={Chaos}, year={1998}, volume={8 2}, pages={ 393-395 } }

We consider a dynamical system with state space M, a smooth, compact subset of some R(n), and evolution given by T(t), x(t)=T(t)x, x in M; T(t) is invertible and the time t may be discrete, t in Z, T(t)=T(t), or continuous, t in R. Here we show that starting with a continuous positive initial probability density rho(x,0)>0, with respect to dx, the smooth volume measure induced on M by Lebesgue measure on R(n), the expectation value of logrho(x,t), with respect to any stationary (i.e., time…

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