Estimates of the rate of convergence in the von Neumann and Birkhoff ergodic theorems

Estimates of the rate of convergence in the von Neumann and Birkhoff ergodic theorems Full article

Journal

Transactions of the Moscow Mathematical Society
ISSN: 0077-1554 , E-ISSN: 1547-738X

Output data

Year: 2016, Volume: 77, Pages: 1-53 Pages count : 53 DOI: 10.1090/mosc/256

Tags

Anosov system; Billiard; Convergence rates in ergodic theorems; Correlation decay; Large deviation decay

Authors

Kachurovskii Aleksandr G. ¹ , Podvigin Ivan V. ²

Affiliations

1	Sobolev Institute of Mathematics
2	Novosibirsk State University

We present estimates (which are necessarily spectral) of the rate of convergence in the von Neumann ergodic theorem in terms of the singularity at zero of the spectral measure of the function to be averaged with respect to the corresponding dynamical system as well as in terms of the decay rate of the correlations (i.e., the Fourier coefficients of this measure). Estimates of the rate of convergence in the Birkhoff ergodic theorem are given in terms of the rate of convergence in the von Neumann ergodic theorem as well as in terms of the decay rate of the large deviation probabilities. We give estimates of the rate of convergence in both ergodic theorems for some classes of dynamical systems popular in applications, including some well-known billiards and Anosov systems.

Kachurovskii A.G. , Podvigin I.V.
Estimates of the rate of convergence in the von Neumann and Birkhoff ergodic theorems
Transactions of the Moscow Mathematical Society. 2016. V.77. P.1-53. DOI: 10.1090/mosc/256 Scopus РИНЦ OpenAlex

Качуровский А.Г. , Подвигин И.В.
Оценки скоростей сходимости в эргодических теоремах фон Неймана и Биркгофа
Труды Московского математического общества. 2016. Т.77. №1. С.1-66. РИНЦ MathNet

Scopus:	2-s2.0-85001930550
Elibrary:	29463820
OpenAlex:	W2558128491

DB	Citing
Scopus	26
Elibrary	17
OpenAlex	23