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Kuzmin, coupling, cones, and exponential mixing. (English) Zbl 1081.28011

The author studies a class of fibred systems with good distortion properties (Gibbs-Markov maps), including folklore maps as well as multidimensional continued fraction algorithms like Jacobi-Perron. Using an elementary coupling scheme based on regularity it is given an easy proof of an exponential uniform convergence (or “Kuzmin type”) theorem for the iterates of the transfer operator. This approach is then shown to be equivalent to the cone contraction method.

MSC:

28D05 Measure-preserving transformations
37A25 Ergodicity, mixing, rates of mixing
37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.
11K50 Metric theory of continued fractions
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References:

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