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 APM  Vol.5 No.9 , July 2015
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.
Keywords: Measure Preserving Maps, Dynamical Systems, Ergodic Theory, Asymptotic Statistics
Cite this paper: Catsigeras, E. (2015) Oscillating Statistics of Transitive Dynamics. Advances in Pure Mathematics, 5, 534-543. doi: 10.4236/apm.2015.59049.
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