Ergodic theory for inner functions of the upper half plane

Jon Aaronson

Annales de l'I.H.P. Probabilités et statistiques (1978)

  • Volume: 14, Issue: 3, page 233-253
  • ISSN: 0246-0203

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Aaronson, Jon. "Ergodic theory for inner functions of the upper half plane." Annales de l'I.H.P. Probabilités et statistiques 14.3 (1978): 233-253. <http://eudml.org/doc/77089>.

@article{Aaronson1978,
author = {Aaronson, Jon},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
language = {eng},
number = {3},
pages = {233-253},
publisher = {Gauthier-Villars},
title = {Ergodic theory for inner functions of the upper half plane},
url = {http://eudml.org/doc/77089},
volume = {14},
year = {1978},
}

TY - JOUR
AU - Aaronson, Jon
TI - Ergodic theory for inner functions of the upper half plane
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1978
PB - Gauthier-Villars
VL - 14
IS - 3
SP - 233
EP - 253
LA - eng
UR - http://eudml.org/doc/77089
ER -

References

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  1. [1] J. Aaronson, Rational Ergodicity. Israel Journal of Mathematics, t. 27, 2, 1977, p. 93-123. Zbl0376.28011MR584018
  2. [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. Zbl0298.28012MR335751
  3. [3] S. Foguel, The ergodic theory of Markov processes. New York, Van-Nostrand Reinhold, 1969. Zbl0282.60037MR261686
  4. [4] S. Foguel and M. Lin, Some ratio limit theorems for Markov operators. Z. Wahrscheinlichkeitstheorie, t. 231, p. 55-66. Zbl0223.60027MR310974
  5. [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. Zbl0347.28015MR372156
  6. [6] G. Letac, Which functions preserve Cauchy laws. P. A. M. S. t. 67, 2,1977, p. 277-286. Zbl0376.28019MR584393
  7. [7] T. Li and F. Schweiger, The generalized Boole transformation is ergodic. Preprint. Zbl0389.28009
  8. [8] M. Lin, Mixing for Markov operators. Z. Wahrscheinlichkeitstheorie, t. 19, 3, 1971, p. 231-243. Zbl0212.49301MR309207
  9. [9] W. Rudin, Real and Complex analysis. McGraw Hill, 1966. Zbl0142.01701MR210528
  10. [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. Zbl0348.28016MR447162
  11. [11] F. Schweiger, Tan x is ergodic. To appear in P. A. M. S. Zbl0361.28011MR2005886
  12. [12] K. Yosida, Functional analysis. Springer, Berlin, 1968. MR239384
  13. [13] A. Denjoy, Fonctions contractent le cercle | Z | &lt; 1, C. R. Acad. Sci. Paris, t. 182, 1926, p. 255-257. 
  14. [14] M. Heins, On the pseudo periods of the weierstrass Zeta function, Nagaoya Math. Journal, t. 30, 1967, p. 113-119. Zbl0177.34903MR262492
  15. [15] J.H. Neuwirth, Ergodicity of some mapping of the circle and the line, preprint. MR516157
  16. [16] F. Schweiger and M. Thaler, Ergodische Eigenschaften einer Klass reellen Transformationen, preprint. MR254007
  17. [17] M. Tsuji, Potential theory in modern function theory, Maruzen, Tokyo, 1959. Zbl0087.28401MR114894
  18. [18] J. Wolff, Sur l'itération des fonctions holomorphes dans une region, C. R. Acad. Sci. Paris, t. 182, 1926, p. 42-43. Zbl52.0309.02JFM52.0309.02

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