Search and download archives of mathematical journals

  Table of contents for this issue | Next article
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, 79 (1994), p. 5-46
Full text djvu | pdf | Reviews MR 96a:58157 | Zbl 0839.54029 | 3 citations in Numdam

stable URL:


[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.  Zbl 0007.21502 |  JFM 59.0344.02
[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.
Article |  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.
Article |  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.
Article |  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.
Article |  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).
Copyright Cellule MathDoc 2016 | Credit | Site Map