Geodesic
The maximum pointwise rate of convergence in Birkhoff's ergodic theorem
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 498 (2020), pp. 18-25 Cet article a éte moissonné depuis la source Math-Net.Ru

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A criterion for the maximum possible pointwise convergence rate in Birkhoff's ergodic theorem for ergodic semiflows in a Lebesgue space is obtained. It is proved that higher rates of convergence in this theorem are impossible. 
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A. G. Kachurovskii; I. V. Podvigin; A. A. Svishchev. The maximum pointwise rate of convergence in Birkhoff's ergodic theorem. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 498 (2020), pp. 18-25. http://geodesic.mathdoc.fr/item/ZNSL_2020_498_a1/

[1] U. Krengel, “On the speed of convergence in the ergodic theorem”, Monatsh. Math., 86:1 (1978), 3–6 | DOI | MR | Zbl

[2] A. G. Kachurovskii, “Skorosti skhodimosti v ergodicheskikh teoremakh”, UMN, 51:4 (1996), 73–124 | MR | Zbl

[3] A. G. Kachurovskii, I. V. Podvigin, “Ob izmerenii skorostei skhodimosti v ergodicheskoi teoreme Birkgofa”, Mat. zametki, 106:1 (2019), 40–52 | MR | Zbl

[4] A. G. Kachurovskii, I. V. Podvigin, “Otsenki skorostei skhodimosti v ergodicheskikh teoremakh fon Neimana i Birkgofa”, Tr. MMO, 77, no. 1, 2016, 1–66 | Zbl

[5] V. A. Rokhlin, “Ob osnovnykh ponyatiyakh teorii mery”, Mat. sb., 25(67):1 (1949), 107–150 | Zbl

[6] Ya. G. Sinai, Sovremennye problemy ergodicheskoi teorii, Fizmatlit, M., 1995

[7] I. Ya. Shneiberg, “Nuli integralov vdol traektorii ergodicheskikh sistem”, Funkts. anal. i ego pril., 19:2 (1985), 92–93 | MR | Zbl

[8] B. Marcus, K. Petersen, “Balancing ergodic averages”, Ergodic Theory, Proc. Conf., Math. Forschungsinst. (Oberwolfach, Germany, 1978), Lecture Notes Math., 729, Springer-Verlag, Berlin, 1979, 126–143 | DOI | MR

[9] U. Krengel, Ergodic Theorems, Walter de Gruyter, Berlin–New York, 1985 | MR | Zbl

[10] V. A. Rokhlin, “Izbrannye voprosy metricheskoi teorii dinamicheskikh sistem”, UMN, 4:2 (1949), 57–128 | MR | Zbl