TY - JOUR

T1 - Estimates for Correlation in Dynamical Systems

T2 - From Hölder Continuous Functions to General Observables

AU - Podvigin, I. V.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - For many dynamical systems that are popular in applications, estimates are known for the decay of correlation in the case of Hölder continuous functions. In the present article, we suggest an approach that allows us to obtain estimates for correlation in dynamical systems in the case of arbitrary functions. This approach is based on approximation and estimates are obtained with the use of known estimates for Hölder continuous functions. We apply our approach to transitive Anosov diffeomorphisms and derive the central limit theorem for the characteristic functions of certain sets with boundary of zero measure.

AB - For many dynamical systems that are popular in applications, estimates are known for the decay of correlation in the case of Hölder continuous functions. In the present article, we suggest an approach that allows us to obtain estimates for correlation in dynamical systems in the case of arbitrary functions. This approach is based on approximation and estimates are obtained with the use of known estimates for Hölder continuous functions. We apply our approach to transitive Anosov diffeomorphisms and derive the central limit theorem for the characteristic functions of certain sets with boundary of zero measure.

KW - Anosov diffeomorphisms

KW - approximation spaces

KW - central limit theorem

KW - correlation

KW - the best approximation

UR - http://www.scopus.com/inward/record.url?scp=85052114693&partnerID=8YFLogxK

U2 - 10.3103/S1055134418030045

DO - 10.3103/S1055134418030045

M3 - Article

AN - SCOPUS:85052114693

VL - 28

SP - 187

EP - 206

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 3

ER -