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arXiv · 1502.04400

Oscillating statistics of transitive dynamics

Eleonora Catsigeras
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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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Eleonora Catsigeras. 2015-06-13. Oscillating statistics of transitive dynamics. https://doi.org/10.4236/apm.2015.59049

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