Poison Limit for Two-Dimensional Toral Automorphism Driven by Continued Fractions

M. Gordin, M. Denker

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)139-149
Number of pages11
JournalJournal of Mathematical Sciences (United States)
Volume199
Issue number2
DOIs
StatePublished - Jun 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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