Abstract
An exposition of some methods of proving exponential (stretched exponential) decay of correlations is given. One-dimensional strictly hyperbolic and quadratic maps and two-dimensional piecewise smooth, uniformly hyperbolic maps are considered. The emphasis is on the fundamental constructions of the Markov sieve method due to Bunimovich-Chernov-Sinai and those of Liverani's Hilbert metric method.
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Krámli, A. Decay of correlations in one and two dimensions. J Stat Phys 83, 167–191 (1996). https://doi.org/10.1007/BF02183644
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DOI: https://doi.org/10.1007/BF02183644