Author(s)

Eleonora Catsigeras

Instituto de Matemática y Estadística “Rafael Laguardia”, Universidad de la República, Montevideo, Uruguay.

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.

Measure Preserving Maps, Dynamical Systems, Ergodic Theory, Asymptotic Statistics

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