Ergodic theory for inner functions of the upper half plane
Annales de l'I.H.P. Probabilités et statistiques, Volume 14 (1978) no. 3, p. 233-253
@article{AIHPB_1978__14_3_233_0,
     author = {Aaronson, Jon},
     title = {Ergodic theory for inner functions of the upper half plane},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     publisher = {Gauthier-Villars},
     volume = {14},
     number = {3},
     year = {1978},
     pages = {233-253},
     zbl = {0378.28009},
     mrnumber = {508928},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1978__14_3_233_0}
}
Aaronson, Jon. Ergodic theory for inner functions of the upper half plane. Annales de l'I.H.P. Probabilités et statistiques, Volume 14 (1978) no. 3, pp. 233-253. http://www.numdam.org/item/AIHPB_1978__14_3_233_0/

[1] J. Aaronson, Rational Ergodicity. Israel Journal of Mathematics, t. 27, 2, 1977, p. 93-123. | MR 584018 | Zbl 0376.28011

[2] R. Adler and B. Weiss, The ergodic, infinite measure preserving transformation of Boole. Israel Journal of Mathematics, t. 16, 3, 1973, p. 263-278. | MR 335751 | Zbl 0298.28012

[3] S. Foguel, The ergodic theory of Markov processes. New York, Van-Nostrand Reinhold, 1969. | MR 261686 | Zbl 0282.60037

[4] S. Foguel and M. Lin, Some ratio limit theorems for Markov operators. Z. Wahrscheinlichkeitstheorie, t. 231, p. 55-66. | MR 310974 | Zbl 0223.60027

[5] J.H.B. Kemperman, The ergodic behaviour of a class of real transformations. Stochastic Processes and related topics. Proceedings of the summer research institute on statistical inference for stochastic processes (Editor Puri), Indiana University, p. 249-258, Academic Press, 1975. | MR 372156 | Zbl 0347.28015

[6] G. Letac, Which functions preserve Cauchy laws. P. A. M. S. t. 67, 2,1977, p. 277-286. | MR 584393 | Zbl 0376.28019

[7] T. Li and F. Schweiger, The generalized Boole transformation is ergodic. Preprint.

[8] M. Lin, Mixing for Markov operators. Z. Wahrscheinlichkeitstheorie, t. 19, 3, 1971, p. 231-243. | MR 309207 | Zbl 0212.49301

[9] W. Rudin, Real and Complex analysis. McGraw Hill, 1966. | MR 210528 | Zbl 0142.01701

[10] F. Schweiger, Zahlentheoretische transformation mit σ-endlichen mass. S.-Ber. Ost. Akad. Wiss., Math.-naturw. K. l., II. Abt., t. 185, 1976, p. 95-103. | MR 447162 | Zbl 0348.28016

[11] F. Schweiger, Tan x is ergodic. To appear in P. A. M. S. | MR 2005886 | Zbl 0361.28011

[12] K. Yosida, Functional analysis. Springer, Berlin, 1968. | MR 239384

[13] A. Denjoy, Fonctions contractent le cercle | Z | < 1, C. R. Acad. Sci. Paris, t. 182, 1926, p. 255-257.

[14] M. Heins, On the pseudo periods of the weierstrass Zeta function, Nagaoya Math. Journal, t. 30, 1967, p. 113-119. | MR 262492 | Zbl 0177.34903

[15] J.H. Neuwirth, Ergodicity of some mapping of the circle and the line, preprint. | MR 516157

[16] F. Schweiger and M. Thaler, Ergodische Eigenschaften einer Klass reellen Transformationen, preprint. | MR 254007

[17] M. Tsuji, Potential theory in modern function theory, Maruzen, Tokyo, 1959. | MR 114894 | Zbl 0087.28401

[18] J. Wolff, Sur l'itération des fonctions holomorphes dans une region, C. R. Acad. Sci. Paris, t. 182, 1926, p. 42-43. | JFM 52.0309.02