Spectrum of the Ruelle operator and exponential decay of correlations for open billiard flows

By L. Stoyanov. 2001

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Expanding maps on Cantor sets and analytic continuation of zeta functions (2005, background): “The ideas are similar to [41], but we have to deal here with a more general family of Cantor sets where the number of subcylinders of a given cylinder may not be constant, in contrast to the case of open billiards in [41].”
Chapter 2 – Smooth Ergodic Theory and Nonuniformly Hyperbolic Dynamics (2006, methodology): “We end this section by mentioning the works of Pollicott [206] and Baladi & Vallée [19] for versions of Dolgopyat’s estimate for semi-flows over piecewise expanding maps of the interval, Dolgopyat’s study of exponential and rapid mixing for generic hyperbolic flows [73, 75], the paper by Stoyanov [2”