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Zap. Nauchn. Sem. POMI, 2016, Volume 448, Pages 177–200 (Mi znsl6311)  

Limiting curves for polynomial adic systems

A. R. Minabutdinov

National Research University "Higher School of Economics", St. Petersburg Branch, St. Petersburg, Russia

Abstract: We prove the existence of limiting curves (describing deviations in the ergodic theorem) for cylinder functions for polynomial adic systems. For a general ergodic measure-preserving transformation and a summable function, we give a necessary condition for a limiting curve to exist. Our work generalizes results by E. Janvresse, T. de la Rue, and Y. Velenik.

Key words and phrases: polynomial adic systems, ergodic theorem, deviations in ergodic theorem.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00373


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English version:
Journal of Mathematical Sciences (New York), 2017, 224:2, 286–303

Bibliographic databases:

UDC: 517.987.5+519.21
Received: 25.09.2016

Citation: A. R. Minabutdinov, “Limiting curves for polynomial adic systems”, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Zap. Nauchn. Sem. POMI, 448, POMI, St. Petersburg, 2016, 177–200; J. Math. Sci. (N. Y.), 224:2 (2017), 286–303

Citation in format AMSBIB
\Bibitem{Min16}
\by A.~R.~Minabutdinov
\paper Limiting curves for polynomial adic systems
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXVII
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 448
\pages 177--200
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6311}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3576258}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 2
\pages 286--303
\crossref{https://doi.org/10.1007/s10958-017-3415-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019693472}


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