Hubbard, John H.; Oberste-Vorth, Ralph W.
Hénon mappings in the complex domain I : the global topology of dynamical space
Publications Mathématiques de l'IHÉS, Tome 79 (1994) , p. 5-46
Zbl 0839.54029 | MR 96a:58157 | 3 citations dans Numdam
URL stable : http://www.numdam.org/item?id=PMIHES_1994__79__5_0

Bibliographie

[A] Ahlfors, L., Conformal Invariants, McGraw-Hill, New York, 1973. Zbl 0272.30012

[B] Bedford, E., Iteration of polynomial automorphisms of C2, Proceedings of the International Congress of Mathematicians, 1990, Kyoto, Japan, Springer-Verlag, Tokyo, Japan, 1991, 847-858. MR 93b:32039 | Zbl 0746.58040

[BS1] Bedford, E. and Smillie, J., Polynomial diffeomorphisms of C2 : currents, equilibrium measure, and hyperbolicity, Invent. Math., 103 (1991), 69-99. | MR 92a:32035 | Zbl 0721.58037

[BS2] Bedford, E. and Smillie, J., Fatou-Bieberbach domains arising from polynomial automorphisms, Indiana U. Math. J., 40 (1991), 789-792. MR 92k:32044 | Zbl 0739.32027

[BS3] Bedford, E. and Smillie, J., Polynomial diffeomorphisms of C2, II : Stable manifolds and recurrence, J. Amer. Math. Soc., 4 (1991), 657-679. MR 92m:32048 | Zbl 0744.58068

[BS4] Bedford, E. and Smillie, J., Polynomial diffeomorphisms of C2, III : Ergodicity, exponents, and entropy of the equilibrium measure, Math. Ann. (to appear). | Zbl 0765.58013

[BLS] Bedford, E., Lyubich, M. and Smillie, J., Polynomial diffeomorphisms of C2, IV : The measure of maximal entropy and laminar currents, (to appear). Zbl 0792.58034

[BC] Benedicks, M. and Carleson, L., The dynamics of the Hénon map, Ann. Math., 133 (1991), 73-169. MR 92d:58116 | Zbl 0724.58042

[Bi] Bieberbach, L., Beispiel zweier ganzer Funktionen zweier komplexer Variabeln, welche eine schlicht volumetreue Abbildung des R4 auf einen Teil seiner selbst vermitteln, Sitzungsber. Preuss. Akad. Wiss. Berlin, Phys-math. Kl. (1933), 476-479. JFM 59.0344.02 | Zbl 0007.21502

[BH] Branner, B., Hubbard, J., The dynamics of cubic polynomials, II : Patterns and parapatterns, Acta Math., 169 (1992), 229-325. MR 94d:30044 | Zbl 0812.30008

[Br] Brolin, H., Invariant sets under iteration of rational functions, Ark. Math., 6 (1965), 103-144. MR 33 #2805 | Zbl 0127.03401

[D] Dold, A., Fixed point index and fixed point theorem for Euclidean neighborhood retracts, Topology, 4 (1965), 1-8. MR 33 #1850 | Zbl 0135.23101

[DH] Douady, A. et Hubbard, J., Etude dynamique des polynômes complexes, Publications mathématiques d'Orsay, Université de Paris-Sud (1984-1985). Zbl 0552.30018

[EE] Earle, C. and Eells, J., A fibre bundle description of Teichmüller theory, J. Diff. Geom., 3 (1969), 33-41. MR 43 #2737a | Zbl 0185.32901

[F] Fatou, P., Sur les fonctions méromorphes de deux variables, C. R. Acad. Sc. Paris, 175 (1922), 862-865 ; Sur certaines fonctions uniformes de deux variables, ibid., 175 (1922), 1030-1033. JFM 48.0391.02

[FS] Fornæss, J. and Sibony, N., Complex Hénon mappings in C2 and Fatou-Bieberbach domains, Duke Math. J., 65 (1992), 345-380. Zbl 0761.32015

[FM] Friedland, S. and Milnor, J., Dynamical properties of plane polynomial automorphisms, Ergod Th. & Dynam. Syst., 9 (1989), 67-99. MR 90f:58163 | Zbl 0651.58027

[G] Gunning, R., Introduction to Holomorphic Functions of Several Variables, Vol. III : Homological Theory, Wadsworth & Brooks/Cole, Belmont, CA, 1990. Zbl 0699.32001

[Ha] Hamstrom, M., Homotopy groups of the space of homeomorphisms, Ill. J. Math., 10 (1966), 563-573. MR 34 #2014 | Zbl 0151.33002

[Hé1] Hénon, M., Numerical study of quadratic area preserving mappings, Q. Appl. Math., 27 (1969), 291-312. MR 40 #6727 | Zbl 0191.45403

[Hé2] Hénon, M., A two-dimensional mapping with a strange attractor, Commun. Math. Phys., 50 (1976), 69-77. MR 54 #10917 | Zbl 0576.58018

[Ho] Holmes, P., Bifurcation sequences in horseshoe maps : infinitely many routes to chaos, Phys. Lett. A, 104 (1984), 299-302. MR 85j:58115

[HWh] Holmes, P. and Whitley, R., Bifurcations of one- and two-dimensional maps, Philos. Trans. Roy. Soc. London, Ser. A, 311 (1984), 43-102. MR 87h:58143a | Zbl 0556.58023

[HWi] Holmes, P. and Williams, R., Knotted periodic orbits in suspensions of Smale's horseshoe : torus knots and bifurcation sequences, Arch. Rational Mech. Anal., 90 (1985), 115-194. MR 87h:58142 | Zbl 0593.58027

[H] Hubbard, J., The Hénon mappings in the complex domain, in Chaotic Dynamics and Fractals (M. Barnsley and S. Demko, ed.), Academic Press, New York, 1986, pp. 101-111. MR 858009 | Zbl 0601.32029

[HY] Hubbard, J., Local connectivity of Julia sets and bifurcation loci : three theorems of J.-C. Yoccoz, in Topological Methods in Modern Mathematics : A Symposium in Honor of John Milnor's Sixtieth Birthday, Publish or Perish, Houston, Texas, 1993, pp. 467-511. MR 94c:58172 | Zbl 0797.58049

[HO] Hubbard, J. and Oberste-Vorth, R., Hénon mappings in the complex domain, II : projective and inductive limits of polynomials, in Real and Complex Dynamics, Kluwer, Amsterdam, 1994.

[M1] Milnor, J., Non-expansive Hénon maps, Adv. in Math., 69 (1988), 109-114. MR 89g:58174 | Zbl 0647.58043

[M2] Milnor, J., Dynamics in one complex variable : introductory lectures, preprint, Institute for Mathematical Sciences, SUNY, Stony Brook (1990).

[MV] Mora, L. and Viana, M., Abundance of strange attractors, Acta Math. (to appear). Zbl 0815.58016

[O] Oberste-Vorth, R., Complex horseshoes (to appear).

[Sm] Smale, S., Differentiable dynamical systems, Bull. Amer. Math. Soc., 73 (1967), 747-817 ; reprinted in The Mathematics of Time, Springer-Verlag, New York, 1980. MR 37 #3598 | Zbl 0202.55202

[S] Smillie, J., The entropy of polynomial diffeomorphisms of C2, Ergod. Th. and Dynam. Syst., 10 (1990), 823-827. MR 92b:58131 | Zbl 0695.58023

[T] Thurston, W., The combinatorics of rational maps (to appear).

[vD] Van Dantzig, D., Über topologisch homogene Kontinua, Fund. Math., 14 (1930), 102-105. JFM 56.1130.01

[V] Vietoris, L., Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen, Math. Ann., 97 (1927), 454-472. JFM 53.0552.01

[W] Williams, R., One-dimensional nonwandering sets, Topology, 6 (1967), 473-487. MR 36 #897 | Zbl 0159.53702

[Y] Yoccoz, J., Sur la connectivité locale de M, unpublished (1989).