Research output: Contribution to journal › Article › peer-review
Estimates for Correlation in Dynamical Systems : From Hölder Continuous Functions to General Observables. / Podvigin, I. V.
In: Siberian Advances in Mathematics, Vol. 28, No. 3, 01.07.2018, p. 187-206.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 16265764