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Exponential decay of correlations for surface semi-flows without finite Markov partitions. (English) Zbl 1055.37027
An important bound for the norms of iterates of the transfer operator associated to piecewise uniformly expanding \(C^2\) interval maps due to D. Dolgopyat [Ann. Math. (2) 147, 357–390 (1998; Zbl 0911.58029)] is extended from finitely many intervals of monotonicity to infinitely many intervals. This may ultimately be useful for extending results on exponential decay of correlations in the setting of billiards.

37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.
37D50 Hyperbolic systems with singularities (billiards, etc.) (MSC2010)
Full Text: DOI
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