%0 Journal Article
%T Oscillating Statistics of Transitive Dynamics
%A Eleonora Catsigeras
%J Advances in Pure Mathematics
%P 534-543
%@ 2160-0384
%D 2015
%I Scientific Research Publishing
%R 10.4236/apm.2015.59049
%X We prove that topologically generic orbits of <em>C</em><sup>0</sup> , 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 <em>f</em> is ergodic with respect to the Lebesgue measure, then also Lebesgue-almost all the orbits exhibit that kind of extremely oscillating statistics.
%K Measure Preserving Maps
%K Dynamical Systems
%K Ergodic Theory
%K Asymptotic Statistics
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=57756