Positive measure sets of ergodic rational maps

Mary Rees

Annales scientifiques de l'École Normale Supérieure (1986)

  • Volume: 19, Issue: 3, page 383-407
  • ISSN: 0012-9593

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Rees, Mary. "Positive measure sets of ergodic rational maps." Annales scientifiques de l'École Normale Supérieure 19.3 (1986): 383-407. <http://eudml.org/doc/82180>.

@article{Rees1986,
author = {Rees, Mary},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {ergodicity; invariant measures equivalent to Lebesgue measure; analytic family of rational maps},
language = {eng},
number = {3},
pages = {383-407},
publisher = {Elsevier},
title = {Positive measure sets of ergodic rational maps},
url = {http://eudml.org/doc/82180},
volume = {19},
year = {1986},
}

TY - JOUR
AU - Rees, Mary
TI - Positive measure sets of ergodic rational maps
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1986
PB - Elsevier
VL - 19
IS - 3
SP - 383
EP - 407
LA - eng
KW - ergodicity; invariant measures equivalent to Lebesgue measure; analytic family of rational maps
UR - http://eudml.org/doc/82180
ER -

References

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  1. [B-C] M. BENEDICKS and L. CARLESON, On Iterations of l-ax2 on (-1, 1), Institut Mittag-Leffler, Report No. 3, 1983. 
  2. [B] H. BROLIN, Invariant Sets Under Iteration of Rational Functions, (Arkiv for Mathmatik, Vol. 6, 1965, pp. 103-144). Zbl0127.03401MR33 #2805
  3. [D] P. L. DUREN, Univalent Functions, New York, Springer, 1983. Zbl0514.30001MR85j:30034
  4. [F] P. FATOU, Sur les équations fonctionnelles (Bull. Soc. Math. Fr., Vol. 47, 1919, pp. 161-271 and Vol. 48, 1920, pp. 33-94 and pp. 208-314). Zbl47.0921.02JFM47.0921.02
  5. [H 1] M. R. HERMAN, Construction d'un difféomorphisme minimal d'entropie topologique non nulle (Erg. Theory and Dynam. Syst., Vol. 1, 1981, pp. 65-76). Zbl0469.58008MR83c:58046
  6. [H 2] M. R. HERMAN, Une méthode pour minorer les exposants de Lyapunov et quelques exemples montrant le caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2 (to appear). Zbl0554.58034
  7. [J] M. V. JABOBSON, Absolutely Continuous Invariant Measures for One-Parameter Families of One-Dimensional Maps (Comm. in Math. Phys., Vol. 81, 1981, pp. 39-88). Zbl0497.58017MR83j:58070
  8. [M-S-S] R. MANÉ, P. SAD and D. SULLIVAN, On the Dynamics of Rational Maps (Ann. Éc. Norm. Sup., Vol. 16, 1983, pp. 193-217). Zbl0524.58025MR85j:58089
  9. [R] M. REES, Ergodic Rational Maps with Dense Critical Point Forward Orbit (Erg. Theory and Dynam. Syst., Vol. 4, 1984, pp. 311-322). Zbl0553.58008MR85m:58111
  10. [S 1] D. SULLIVAN, Conformal Dynamical Systems, Geometric Dynamics, (Lecture Notes in Math., No. 1007, 1981, pp. 725-752). Zbl0524.58024MR85m:58112
  11. [S 2] D. SULLIVAN, Quasi-Conformal Homeomorphisms and Dynamics I (to appear). 
  12. [SZ] W. SZLENK, Some Dynamical Properties of Certain Differentiable Mappings of an Interval (Bol. Soc. Mat. Mex., Vol. 24, No. 2, 1979, pp. 57-82). Zbl0487.58013MR83c:58048

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