Oscillating statistics of transitive dynamics
arXiv:1502.04400 · doi:10.4236/apm.2015.59049
Abstract
We prove that topologically generic orbits of C0 transitive and non-uniquely ergodic dynamical systems, exhibit an extremely oscillating asymptotical statistics. Precisely, the minimum weak* compact set of invariant probabilities, that describes the asymptotical statistics of each orbit of a residual set, contains all the ergodic probabilities. If besides f is ergodic with respect to the Lebesgue measure, then also Lebesgue-almost all the orbits exhibit that kind of extremely oscillating statistics.
arXiv commentThis revised version has some new paragraphs at the introduction according to the suggestion of the referee