Geodesic
Operator Ergodic Theorems for Actions of Free Semigroups and Groups
Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 4, pp. 1-17.

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New ergodic theorems are obtained for measure-preserving actions of free semigroups and groups. These theorems are derived from ergodic theorems for Markov operators. This approach also allows one to obtain ergodic theorems for some classes of Markov semigroups. Results of the paper generalize classical ergodic theorems of Kakutani, Oseledets, and Guivarc'h, and recent ergodic theorems of Grigorchuk, Nevo, and Nevo and Stein. 
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A. I. Bufetov. Operator Ergodic Theorems for Actions of Free Semigroups and Groups. Funkcionalʹnyj analiz i ego priloženiâ, Tome 34 (2000) no. 4, pp. 1-17. http://geodesic.mathdoc.fr/item/FAA_2000_34_4_a0/

[1] Gromov M., “Hyperbolic groups”, Essays in Group Theory, Math. Sci. Res. Inst. Publ., 8, ed. Gersten S. M., Springer-Verlag, New York, 1987, 75–263 | MR

[2] Oseledets V. I., “Markovskie tsepi, kosye proizvedeniya i ergodicheskie teoremy dlya obschikh dinamicheskikh sistem”, Teoriya veroyatnostei i ee primeneniya, 10:3 (1965), 551–557 | MR | Zbl

[3] Kakutani S., “Random ergodic theorems and Markoff processes with a stable distribution”, Proc. 2nd Berkeley Symposium Math. Stat. and Prob., University of California Press, Berkeley and Los Angeles, 1951, 247–261 | MR

[4] Vershik A. M., “Dinamicheskaya teoriya rosta v gruppakh: entropiya, granitsy, primery”, UMN, 55:4 (2000), 59–128 | DOI | MR | Zbl

[5] Vershik A. M., Nechaev S., Bikbov R., Statistical properties of braid groups in locally free approximation, Preprint IHES/M/99/45, June 1999

[6] Vershik A. M., “Chislennye kharakteristiki grupp i sootnosheniya mezhdu nimi”, Zapiski nauchnykh seminarov POMI, 256, 1999, 5–18 | MR | Zbl

[7] Grigorchuk R. I., “Individualnaya ergodicheskaya teorema dlya deistvii svobodnykh grupp”, Tezisy Tambovskoi shkoly po teorii funktsii, 1986 | Zbl

[8] Grigorchuk R. I., “Ergodicheskie teoremy dlya deistvii svobodnoi gruppy i svobodnoi polugruppy”, Matem. zametki, 65:5 (1999), 779–782 | DOI | MR

[9] Arnold V. I., Krylov A. L., “Ravnomernoe raspredelenie tochek na sfere i nekotorye ergodicheskie svoistva reshenii lineinykh obyknovennykh differentsialnykh uravnenii v kompleksnoi oblasti”, DAN SSSR, 148:1 (1963), 9–12 | MR

[10] Grigorenko L. A., “O $si$-algebre simmetrichnykh sobytii dlya schetnoi tsepi Markova”, Teoriya veroyatnostei i ee primeneniya, 24:1 (1979), 198–204 | MR | Zbl

[11] Bezhaeva Z. I., Oseledets V. I., “O simmetrichnoi sigma-algebre statsionarnogo markovskogo kharissovskogo protsessa”, Teoriya veroyatnostei i ee primeneniya, 41:4 (1996), 869–877 | DOI | MR | Zbl

[12] Dunford N., Schwartz J. T., “Convergence almost everywhere of operator averages”, J. Rational Mech. Anal., 5 (1956), 129–178 | MR | Zbl

[13] Hopf E., “The general temporarily discrete Markoff process”, J. Rational Mech. Anal., 3 (1954), 13–45 | MR | Zbl

[14] Kolmogorov A. N., “Lokalnaya predelnaya teorema dlya klassicheskikh tsepei Markova”, Izv. AN SSSR, 13:4 (1949), 281–300 | MR | Zbl

[15] Gurevich B. M., “Lokalnaya predelnaya teorema dlya tsepei Markova i usloviya tipa regulyarnosti”, Teoriya veroyatnostei i ee primeneniya, 13:1 (1968), 183–190 | Zbl

[16] Nevo A., “Harmonic analysis and pointwise ergodic theorems for non-commuting transformations”, J. Amer. Math. Soc., 7 (1994), 875–902 | DOI | MR | Zbl

[17] Cannon J., “The combinatorial structure of cocompact discrete hyperbolic groups”, Geom. Dedicata, 16 (1984), 123–148 | DOI | MR | Zbl

[18] Nevo A., Stein E. M., “A generalization of Birkhoff's pointwise ergodic theorem”, Acta Math., 173 (1994), 135–154 | DOI | MR | Zbl

[19] Guivarc'h Y., “Généralisation d'un théorème de von Neumann”, C. R. Acad. Sci Paris, 268 (1969), 1020–1023 | MR

[20] Lorch E. R., “Means of iterated transformations in reflexive vector spaces”, Bull. Amer. Math. Soc., 45 (1939), 945–947 | DOI | MR | Zbl

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

[22] Bufetov A. I., “Ergodicheskie teoremy dlya neskolkikh otobrazhenii”, UMN, 54:4 (1999), 159–160 | DOI | MR | Zbl

[23] Akcoglu M., “A pointwise ergodic theorem in $L_p$-spaces”, Canad. J. Math., 27 (1975), 1075–1082 | DOI | MR | Zbl