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Dynamics of flows and maps (continuous and discrete time), including infinite-dimensional dynamics, Hamiltonian dynamics, ergodic theory.

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Kac's lemma for amenable group actions

The classical Kac's lemma says the following. Let $(X,\mu)$ be a probability space and $T$ a measure preserving transformation. Assume $A\subset X$ has positive measure. Then $$\sum_{k\ge 1} k\mu(A_k …
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