Entropy and Poincaré recurrence from a geometrical viewpoint
arXiv:0809.2938 · doi:10.1088/0951-7715/22/10/003
Abstract
We study Poincaré recurrence from a purely geometrical viewpoint. We prove that the metric entropy is given by the exponential growth rate of return times to dynamical balls. This is the geometrical counterpart of Ornstein-Weiss theorem. Moreover, we show that minimal return times to dynamical balls grow linearly with respect to its length. Finally, some interesting relations between recurrence, dimension, entropy and Lyapunov exponents of ergodic measures are given.
11 pages, revised version