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Dynamical systems on measure spaces, invariant measures, ergodic averages, mixing properties.

1 vote
1 answer
254 views

Question about B. Host paper 'Nombres, normaux entropie, translations'

I put this question on mathstack but it seems more suitable to put it here: I was reading this paper and I got stuck in a detail left for the reader that I couldn't figure out: Let $X = \mathbb{R}/\ …
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8 votes
3 answers
651 views

Classes of dynamical systems

A consequence of Birkhoff ergodic theorem tells us that ergodicity is equivalent to: $\forall A,B \in \mathcal{B} \quad \frac{1}{N}\sum_{n=0}^{N-1}\mu(A\cap T^{-n}(B))\stackrel{N\to \infty}{\longrigh …
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  • 257