On iterations of Misiurewicz's rational maps on the Riemann sphere

P. Grzegorczyk; F. Przytycki; W. Szlenk

Annales de l'I.H.P. Physique théorique (1990)

  • Volume: 53, Issue: 4, page 431-444
  • ISSN: 0246-0211

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Grzegorczyk, P., Przytycki, F., and Szlenk, W.. "On iterations of Misiurewicz's rational maps on the Riemann sphere." Annales de l'I.H.P. Physique théorique 53.4 (1990): 431-444. <http://eudml.org/doc/76515>.

@article{Grzegorczyk1990,
author = {Grzegorczyk, P., Przytycki, F., Szlenk, W.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Riemann sphere; rational map; Julia set; metric exactness; absolutely continuous invariant measure},
language = {eng},
number = {4},
pages = {431-444},
publisher = {Gauthier-Villars},
title = {On iterations of Misiurewicz's rational maps on the Riemann sphere},
url = {http://eudml.org/doc/76515},
volume = {53},
year = {1990},
}

TY - JOUR
AU - Grzegorczyk, P.
AU - Przytycki, F.
AU - Szlenk, W.
TI - On iterations of Misiurewicz's rational maps on the Riemann sphere
JO - Annales de l'I.H.P. Physique théorique
PY - 1990
PB - Gauthier-Villars
VL - 53
IS - 4
SP - 431
EP - 444
LA - eng
KW - Riemann sphere; rational map; Julia set; metric exactness; absolutely continuous invariant measure
UR - http://eudml.org/doc/76515
ER -

References

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  2. [D-H] A. Douady and J. Hubbard, Étude dynamique des polynômes complexes, Publ. Math. Orsay, (2), Vol. 84, (4), p. 85. Zbl0552.30018
  3. [H] E. Hille, Analytic Function Theory, Boston-New York-Chicago-Atlanta-Dallas-Palo Alto-Toronto: Ginn and Company, 1962. Zbl0102.29401MR201608
  4. [Her] M. Herman, Exemples de fractions rationnelles ayant une orbite dense sur la sphère de Riemann, Bull. Soc. Math. France, Vol. 112, 1984, pp. 93-142. Zbl0559.58020MR771920
  5. [Hö] L. Hörmander, An Introduction to Complex Analysis in Several Variables, D. van Nostrand Company Inc., Princeton, New Jersey, 1966. Zbl0138.06203MR203075
  6. [K-S] K. Krzyzewski and W. Szlenk, On Invariant Measures for Expanding Differentiable Mappings, Studia Math., Vol. 33, 1969, pp. 83-92. Zbl0176.00901MR245761
  7. [L] M.Ju. Lyubich, On a Typical Behaviour of Trajectories for a Rational Map of Sphere, Dokl. Ak. N. U.S.S.R., Vol. 268.1, 1982, pp. 29-32. Zbl0595.30034
  8. [M] M. Misiurewicz, Absolutely Continuous Measures for Certain Maps of an Interval, Publications Mathématiques I.H.E.S., Vol. 53, pp. 17-51. Zbl0477.58020MR623533
  9. [R] M. Rees, Positive Measure Sets of Ergodic Rational Maps, Ann. Sci. Éc. Norm. Sup., 4e série, Vol. 19, 1986, pp. 383-407. Zbl0611.58038MR870689
  10. [S] W. Szlenk, Absolutely Continuous Invariant Measures for Rational Mappings of the Sphere S2, Geometric Dynamics (Rio de Janeiro, 1981), pp. 767-783, Lect. Notes Math., Vol. 1007, Springer, Berlin-New York, 1983. Zbl0569.28004MR730298

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