Probabilistic Proofs of Analytic Facts @Turbo - Treat the heat kernel as a transition density as in section 4.1 of the book mentioned in my comment above

Dec
24

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What is known about first return times to Markov partitions for Anosov diffeomorphisms? Thanks for your answer. A bit after I asked this question some physical considerations led me to be primarily concerned with variants of the $L^2$ mixing time and topological entropy as timescales of interest--I still don't know how to define the timescale I really want, but these are close for systems that can't be written as products.