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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.

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