Generalizing powers of a single hyperbolic automorphism of the two-dimensional torus, we consider some class sequences of such automorphism. As a substitute for the pair of foliations in the classical hyperbolic theory, every sequence of this class has a stable family of 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 the Poisson limit theorem for powers of a single hyperbolic automorphism of the torus. Possible generalizations are briefly discussed.
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Translated from Zapiski Nauchnykh Seminarova POMI, Vol. 408, 2012, pp. 131–153.
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Gordin, M., Denker, M. Poison Limit for Two-Dimensional Toral Automorphism Driven by Continued Fractions. J Math Sci 199, 139–149 (2014). https://doi.org/10.1007/s10958-014-1841-z
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DOI: https://doi.org/10.1007/s10958-014-1841-z