Article PDF
Avoid common mistakes on your manuscript.
References
Ahlfors, L.,Conformal Invariants, McGraw-Hill, New York, 1973.
Bedford, E., Iteration of polynomial automorphisms ofC 2,Proceedings of the International Congress of Mathematicians, 1990, Kyoto, Japan, Springer-Verlag, Tokyo, Japan, 1991, 847–858.
Bedford, E. andSmillie, J., Polynomial diffeomorphisms ofC 2: currents, equilibrium measure, and hyperbolicity,Invent. Math.,103 (1991), 69–99.
Bedford, E. andSmillie, J., Fatou-Bieberbach domains arising from polynomial automorphisms,Indiana U. Math. J.,40 (1991), 789–792.
Bedford, E. andSmillie, J., Polynomial diffeomorphisms ofC 2, II: Stable manifolds and recurrence,J. Amer. Math. Soc.,4 (1991), 657–679.
Bedford, E. andSmillie, J., Polynomial diffeomorphisms ofC 2, III: Ergodicity, exponents, and entropy of the equilibrium measure,Math. Ann. (to appear).
Bedford, E., Lyubich, M. andSmillie, J., Polynomial diffeomorphisms ofC 2, IV: The measure of maximal entropy and laminar currents, (to appear).
Benedicks, M. andCarleson, L., The dynamics of the Hénon map,Ann. Math.,133 (1991), 73–169.
Bieberbach, L., Beispiel zweier ganzer Funktionen zweier komplexer Variabeln, welche eine schlicht volumetreue Abbildung desR 4 auf einen Teil seiner selbst vermitteln,Sitzungsber. Preuss. Akad. Wiss. Berlin, Phys.-math. Kl. (1933), 476–479.
Branner, B., Hubbard, J., The dynamics of cubic polynomials, II: Patterns and parapatterns,Acta Math.,169 (1992), 229–325.
Brolin, H., Invariant sets under iteration of rational functions,Ark. Math.,6 (1965), 103–144.
Dold, A., Fixed point index and fixed point theorem for Euclidean neighborhood retracts,Topology,4 (1965), 1–8.
Douady, A. etHubbard, J.,Etude dynamique des polynômes complexes, Publications mathématiques d’Orsay, Université de Paris-Sud (1984–1985).
Earle, C. andEells, J., A fibre bundle description of Teichmüller theory,J. Diff. Geom.,3 (1969), 33–41.
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.
Fornæss, J. andSibony, N., Complex Hénon mappings inC 2 and Fatou-Bieberbach domains,Duke Math. J.,65 (1992), 345–380.
Friedland, S. andMilnor, J., Dynamical properties of plane polynomial automorphisms,Ergod Th. & Dynam. Syst.,9 (1989), 67–99.
Gunning, R.,Introduction to Holomorphic Functions of Several Variables, Vol. III:Homological Theory, Wadsworth & Brooks/Cole, Belmont, CA, 1990.
Hamstrom, M., Homotopy groups of the space of homeomorphisms,Ill. J. Math.,10 (1966), 563–573.
Hénon, M., Numerical study of quadratic area preserving mappings,Q. Appl. Math.,27 (1969), 291–312.
Hénon, M., A two-dimensional mapping with a strange attractor,Commun. Math. Phys.,50 (1976), 69–77.
Holmes, P., Bifurcation sequences in horseshoe maps: infinitely many routes to chaos,Phys. Lett. A,104 (1984), 299–302.
Holmes, P. andWhitley, R., Bifurcations of one- and two-dimensional maps,Philos. Trans. Roy. Soc. London, Ser. A,311 (1984), 43–102.
Holmes, P. andWilliams, R., Knotted periodic orbits in suspensions of Smale’s horseshoe: torus knots and bifurcation sequences,Arch. Rational Mech. Anal.,90 (1985), 115–194.
Hubbard, J., The Hénon mappings in the complex domain, inChaotic Dynamics and Fractals (M. Barnsley and S. Demko, ed.), Academic Press, New York, 1986, pp. 101–111.
Hubbard, J., Local connectivity of Julia sets and bifurcation loci: three theorems of J.-C. Yoccoz, inTopological Methods in Modern Mathematics: A Symposium in Honor of John Milnor’s Sixtieth Birthday, Publish or Perish, Houston, Texas, 1993, pp. 467–511.
Hubbard, J. andOberste-Vorth, R., Hénon mappings in the complex domain, II: projective and inductive limits of polynomials, inReal and Complex Dynamics, Kluwer, Amsterdam, 1994.
Milnor, J., Non-expansive Hénon maps,Adv. in Math.,69 (1988), 109–114.
Milnor, J.,Dynamics in one complex variable: introductory lectures, preprint, Institute for Mathematical Sciences,suny, Stony Brook (1990).
Mora, L. andViana, M., Abundance of strange attractors,Acta Math. (to appear).
Oberste-Vorth, R.,complex horseshoes (to appear).
Smale, S., Differentiable dynamical systems,Bull. Amer. Math. Soc.,73 (1967), 747–817; reprinted inThe Mathematics of Time, Springer-Verlag, New York, 1980.
Smillie, J., The entropy of polynomial diffeomorphisms ofC 2,Ergod. Th. and Dynam. Syst.,10 (1990), 823–827.
Thurston, W.,The combinatorics of rational maps (to appear).
van Dantzig, D., Über topologisch homogene Kontinua,Fund. Math.,14 (1930), 102–105.
Vietoris, L., Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen,Math. Ann.,97 (1927), 454–472.
Williams, R., One-dimensional nonwandering sets,Topology,6 (1967), 473–487.
Yoccoz, J.,Sur la connectivité locale de M, unpublished (1989).
Author information
Authors and Affiliations
About this article
Cite this article
Hubbard, J.H., Oberste-Vorth, R.W. Hénon mappings in the complex domain I: The global topology of dynamical space. Publications Mathématiques de L’Institut des Hautes Scientifiques 79, 5–46 (1994). https://doi.org/10.1007/BF02698886
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02698886