TITLE:
Oscillating Statistics of Transitive Dynamics
AUTHORS:
Eleonora Catsigeras
KEYWORDS:
Measure Preserving Maps, Dynamical Systems, Ergodic Theory, Asymptotic Statistics
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.5 No.9,
July
6,
2015
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.