Oscillating Statistics of Transitive Dynamics

DOI: 10.4236/apm.2015.59049   PDF   HTML   XML   2,418 Downloads   2,858 Views  

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.

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Catsigeras, E. (2015) Oscillating Statistics of Transitive Dynamics. Advances in Pure Mathematics, 5, 534-543. doi: 10.4236/apm.2015.59049.

Conflicts of Interest

The authors declare no conflicts of interest.

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