PermalinkSubmitted by David Ruelle on Sat, 05/27/2017 - 09:53

Problem 95: I think that then problem I discussed with Rufus referred to his very natural version of the proof of the rationality of the zeta function for Axiom A using a Markov partition. Can one imitate this proof for the Weil zeta function of a manifold M over a finite field (with periodic points for Frobenius replacing periodic points for hyperbolic diffeo)? I.e. can one find in a natural way a “Markov Partition” on M?

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## Problem 95: I think that then

Problem 95: I think that then problem I discussed with Rufus referred to his very natural version of the proof of the rationality of the zeta function for Axiom A using a Markov partition. Can one imitate this proof for the Weil zeta function of a manifold M over a finite field (with periodic points for Frobenius replacing periodic points for hyperbolic diffeo)? I.e. can one find in a natural way a “Markov Partition” on M?

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