TY - JOUR
T1 - Poison Limit for Two-Dimensional Toral Automorphism Driven by Continued Fractions
AU - Gordin, M.
AU - Denker, M.
N1 - Funding Information:
A part of this paper was completed during the visit of M. Gordin to Pennsylvania State University. M. G. was also partially supported by the Program “Leading Scientific Schools” (project 2504.2014.1), by the RFBR (project 13-01-00256-a), by the Shapiro grant of Pennsylvania State University, and by the National Science Foundation under Grant Number DMS-1008538. M. D. was supported by the National Science Foundation under Grant Number DMS-10008538.
PY - 2014/6
Y1 - 2014/6
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/84902261902
UR - https://www.scopus.com/pages/publications/84902261902#tab=citedBy
U2 - 10.1007/s10958-014-1841-z
DO - 10.1007/s10958-014-1841-z
M3 - Article
AN - SCOPUS:84902261902
SN - 1072-3374
VL - 199
SP - 139
EP - 149
JO - Journal of Mathematical Sciences (United States)
JF - Journal of Mathematical Sciences (United States)
IS - 2
ER -