Geodesic
Poisson limit for two-dimensional toral automorphisms driven by continued fractions
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 18, Tome 408 (2012), pp. 131-153

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Generalizing powers of a single hyperbolic automorphism of the two-dimensional torus, we consider some class of sequences of such automorphisms. Technically such sequences are determined by means of continued fraction expansions of a pair of real numbers. As a substitute for the pair of foliations in the classical hyperbolic theory, every sequence of this class has a sequence of asymptotically stable and a sequence of asymptotically unstable foliations. We prove a kind of the Poisson limit theorem for such sequences extending a method used earlier by A. Sharova and the present authors to prove a Poisson limit theorem for powers of a single hyperbolic automorphisms of the torus. Possible generalizations are briefly discussed. 
@article{ZNSL_2012_408_a8,
     author = {M. Gordin and M. Denker},
     title = {Poisson limit for two-dimensional toral automorphisms driven by continued fractions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     volume = {408},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_408_a8/}
}
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M. Gordin; M. Denker. Poisson limit for two-dimensional toral automorphisms driven by continued fractions. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 18, Tome 408 (2012), pp. 131-153. http://geodesic.mathdoc.fr/item/ZNSL_2012_408_a8/