Hénon mappings in the complex domain I : the global topology of dynamical space
Publications Mathématiques de l'IHÉS, Tome 79 (1994), pp. 5-46.
@article{PMIHES_1994__79__5_0,
     author = {Hubbard, John H. and Oberste-Vorth, Ralph W.},
     title = {H\'enon mappings in the complex domain {I} : the global topology of dynamical space},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {5--46},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {79},
     year = {1994},
     mrnumber = {1307296},
     zbl = {0839.54029},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1994__79__5_0/}
}
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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), pp. 5-46. http://www.numdam.org/item/PMIHES_1994__79__5_0/

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

[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 | Zbl

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

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

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

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

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

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

[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 | Zbl

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

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

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

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

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

[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

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

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

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

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

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

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

[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 | Zbl

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

[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

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

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

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