Hénon mappings in the complex domain I : the global topology of dynamical space

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1. [A] AHLFORS, L., Conformal Invariants, McGraw-Hill, New York, 1973. Zbl0272.30012
2. [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. Zbl0746.58040MR93b:32039
3. [BS1] BEDFORD, E. and SMILLIE, J., Polynomial diffeomorphisms of C2 : currents, equilibrium measure, and hyperbolicity, Invent. Math., 103 (1991), 69-99. Zbl0721.58037MR92a:32035
4. [BS2] BEDFORD, E. and SMILLIE, J., Fatou-Bieberbach domains arising from polynomial automorphisms, Indiana U. Math. J., 40 (1991), 789-792. Zbl0739.32027MR92k:32044
5. [BS3] BEDFORD, E. and SMILLIE, J., Polynomial diffeomorphisms of C2, II : Stable manifolds and recurrence, J. Amer. Math. Soc., 4 (1991), 657-679. Zbl0744.58068MR92m:32048
6. [BS4] BEDFORD, E. and SMILLIE, J., Polynomial diffeomorphisms of C2, III : Ergodicity, exponents, and entropy of the equilibrium measure, Math. Ann. (to appear). Zbl0765.58013
7. [BLS] BEDFORD, E., LYUBICH, M. and SMILLIE, J., Polynomial diffeomorphisms of C2, IV : The measure of maximal entropy and laminar currents, (to appear). Zbl0792.58034
8. [BC] BENEDICKS, M. and CARLESON, L., The dynamics of the Hénon map, Ann. Math., 133 (1991), 73-169. Zbl0724.58042MR92d:58116
9. [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. Zbl0007.21502JFM59.0344.02
10. [BH] BRANNER, B., HUBBARD, J., The dynamics of cubic polynomials, II : Patterns and parapatterns, Acta Math., 169 (1992), 229-325. Zbl0812.30008MR94d:30044
11. [Br] BROLIN, H., Invariant sets under iteration of rational functions, Ark. Math., 6 (1965), 103-144. Zbl0127.03401MR33 #2805
12. [D] DOLD, A., Fixed point index and fixed point theorem for Euclidean neighborhood retracts, Topology, 4 (1965), 1-8. Zbl0135.23101MR33 #1850
13. [DH] DOUADY, A. et HUBBARD, J., Etude dynamique des polynômes complexes, Publications mathématiques d'Orsay, Université de Paris-Sud (1984-1985). Zbl0552.30018
14. [EE] EARLE, C. and EELLS, J., A fibre bundle description of Teichmüller theory, J. Diff. Geom., 3 (1969), 33-41. Zbl0185.32901MR43 #2737a
15. [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. Zbl48.0391.02JFM48.0391.02
16. [FS] FORNÆSS, J. and SIBONY, N., Complex Hénon mappings in C2 and Fatou-Bieberbach domains, Duke Math. J., 65 (1992), 345-380. Zbl0761.32015
17. [FM] FRIEDLAND, S. and MILNOR, J., Dynamical properties of plane polynomial automorphisms, Ergod Th. & Dynam. Syst., 9 (1989), 67-99. Zbl0651.58027MR90f:58163
18. [G] GUNNING, R., Introduction to Holomorphic Functions of Several Variables, Vol. III : Homological Theory, Wadsworth & Brooks/Cole, Belmont, CA, 1990. Zbl0699.32001
19. [Ha] HAMSTROM, M., Homotopy groups of the space of homeomorphisms, Ill. J. Math., 10 (1966), 563-573. Zbl0151.33002MR34 #2014
20. [Hé1] HÉNON, M., Numerical study of quadratic area preserving mappings, Q. Appl. Math., 27 (1969), 291-312. Zbl0191.45403MR40 #6727
21. [Hé2] HÉNON, M., A two-dimensional mapping with a strange attractor, Commun. Math. Phys., 50 (1976), 69-77. Zbl0576.58018MR54 #10917
22. [Ho] HOLMES, P., Bifurcation sequences in horseshoe maps : infinitely many routes to chaos, Phys. Lett. A, 104 (1984), 299-302. MR85j:58115
23. [HWh] HOLMES, P. and WHITLEY, R., Bifurcations of one- and two-dimensional maps, Philos. Trans. Roy. Soc. London, Ser. A, 311 (1984), 43-102. Zbl0556.58023MR87h:58143a
24. [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. Zbl0593.58027MR87h:58142
25. [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. Zbl0601.32029MR858009
26. [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. Zbl0797.58049MR94c:58172
27. [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. 
28. [M1] MILNOR, J., Non-expansive Hénon maps, Adv. in Math., 69 (1988), 109-114. Zbl0647.58043MR89g:58174
29. [M2] MILNOR, J., Dynamics in one complex variable : introductory lectures, preprint, Institute for Mathematical Sciences, SUNY, Stony Brook (1990). 
30. [MV] MORA, L. and VIANA, M., Abundance of strange attractors, Acta Math. (to appear). Zbl0815.58016
31. [O] OBERSTE-VORTH, R., Complex horseshoes (to appear). Zbl1183.37065
32. [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. Zbl0202.55202MR37 #3598
33. [S] SMILLIE, J., The entropy of polynomial diffeomorphisms of C2, Ergod. Th. and Dynam. Syst., 10 (1990), 823-827. Zbl0695.58023MR92b:58131
34. [T] THURSTON, W., The combinatorics of rational maps (to appear). 
35. [vD] VAN DANTZIG, D., Über topologisch homogene Kontinua, Fund. Math., 14 (1930), 102-105. Zbl56.1130.01JFM56.1130.01
36. [V] VIETORIS, L., Über den höheren Zusammenhang kompakter Räume und eine Klasse von zusammenhangstreuen Abbildungen, Math. Ann., 97 (1927), 454-472. Zbl53.0552.01JFM53.0552.01
37. [W] WILLIAMS, R., One-dimensional nonwandering sets, Topology, 6 (1967), 473-487. Zbl0159.53702MR36 #897
38. [Y] YOCCOZ, J., Sur la connectivité locale de M, unpublished (1989). 

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