A compactification of Hénon mappings in C2 as dynamical systems

Acta Mathematica

Volumn 184, Issue 2, 2000, Pages 203-270

  Hubbard, John ^a,b   Papadopol, Peter ^a,c   Veselov, Vladimir ^a  

^a Department of Obstetrics Gynecology   (United States)

^b AIX MARSEILLE UNIVERSITY   (France)

^c GRAND CANYON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039416215     PISSN: 00015962     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02392629     Document Type: Article

References (65)

1. 2, in Proceedings of the International Congress of Mathematicians (Kyoto, 1990), pp. 847-858. Math. Soc. Japan, Tokyo, 1991.
2. 2, IV: The measure of the maximal entropy and laminar currents. Invent. Math., 112 (1993), 77-125.
3. 2. Invent. Math., 114 (1993), 277-288.
4. 2: Currents, equilibrium measure and hyperbolicity. Invent. Math., 103 (1991), 69-99.
5. 2, II: Stable manifolds and recurrence. J. Amer. Math. Soc., 4 (1991), 657-679.
6. 2, III: Ergodicity, exponents and entropy of the equilibrium measure. Math. Ann., 294 (1992), 395-420.
7. 2, V: Critical points and Lyapunov exponents. J. Geom. Anal., 8 (1998), 349-383.
8. 2, VI: Connectivity of J. Ann. of Math., 148 (1998), 695-735.
9. 2, VII: Hyperbolicity and external rays. Ann. Sci. École Norm. Sup. (4), 32 (1999), 455-497.
10. DOUADY, R. & DOUADY, A., Algèbre et théorie galoisiennes, I; II. Cedic/Fernand Nathan, Paris, 1977; 1979.
11. DOUADY, A. & HÉRAULT, L., Arrondissement des variétés à coins. Comment. Math. Helv., 48 (1973), 484-491 (appendix to A. Borel and J.-P. Serre: Corners and arithmetic groups, pp. 436-483).
12. 2. Indiana Univ. Math. J., 45 (1996), 721-772.
13. DLOUSSKY, G., Une construction élémentaire des surfaces d'Inoue-Hirzebruch. Math. Ann., 280 (1988), 663-682.
14. DLOUSSKY, G. & OELJEKLAUS, K., Foliations on compact surfaces containing global spherical shells. Preprint of CMI, Université de Provence, 1997.
15. FRIEDLAND, S. & MILNOR, J., Dynamical properties of polynomial automorphisms. Ergodic Theory Dynamical Systems, 9 (1989), 67-99.
16. FRIEDLAND, S., Entropy of polynomial and rational maps. Ann. of Math., 133 (1991), 359-368.
17. - Oral communication, 1995.
18. - Entropy of algebraic maps, in Proceedings of the Conference in Honor of Jean-Pierre Kahane (Orsay, 1993). J. Fourier Anal. Appl., Special Issue (1995), 215-228.
19. - Entropy of algebraic maps, in Proceedings of the Conference in Honor of Jean-Pierre Kahane (Orsay, 1993). J. Fourier Anal. Appl., Special Issue (1995), 215-228.
20. 2 and Fatou-Bieberbach domains. Duke Math. J., 65 (1992), 345-380.
21. - Complex dynamics in higher dimension, I, in Complex Analytic Methods in Dynamical Systems (Rio de Janeiro, 1992), pp. 201-231. Astérisque, 222. Soc. Math. France, Paris, 1994.
22. - Complex dynamics in higher dimension, I, in Complex Analytic Methods in Dynamical Systems (Rio de Janeiro, 1992), pp. 201-231. Astérisque, 222. Soc. Math. France, Paris, 1994.
23. - Complex dynamics in higher dimension, II, in Modern Methods in Complex Analysis (Princeton, NJ, 1992), pp. 135 182. Ann. of Math. Stud., 137. Princeton Univ. Press, Princeton, NJ, 1995
24. - Complex dynamics in higher dimension, II, in Modern Methods in Complex Analysis (Princeton, NJ, 1992), pp. 135 182. Ann. of Math. Stud., 137. Princeton Univ. Press, Princeton, NJ, 1995
25. - Complex dynamics in higher dimensions, in Complex Potential Theory (Montreal, PQ, 1993), pp. 131-186. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 439. Kluwer, Dordrecht, 1994.
26. - Complex dynamics in higher dimensions, in Complex Potential Theory (Montreal, PQ, 1993), pp. 131-186. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 439. Kluwer, Dordrecht, 1994.
27. GRIFFITHS, P. & HARRIS, J., Principles of Algebraic Geometry. Pure and Applied Mathematics, Wiley-Interscience, New York, 1978.
28. GRAUERT, H., Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann., 146 (1962), 331-368.
29. GRIFFITH, P. A., Infinite Abelian Group Theory. Chicago Lectures in Math., The University of Chicago Press, Chicago, IL-London, 1970.
30. GUNNING, R. C., Introduction to Holomorphic Functions in Several Variables, III: Homological Theory. Wadsworth & Brooks/Cole Math. Ser. Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, 1990.
31. HARTSHORNE, R., Algebraic Geometry. Graduate Texts in Math., 52. Springer-Verlag, New York-Hoidelberg, 1977.
32. HATCHER, A., Topology. To appear.
33. - Notes on 3-dimensional topology. Manuscript in preparation.
34. HEMPEL, J., 3-Manifolds. Ann. of Math. Stud., 86. Princeton Univ. Press, Princeton, NJ, 1976.
35. HÉNON, M., A two-dimensional mapping with a strange attractor. Comm. Math. Phys., 50 (1976), 69-77.
36. HUBBARD, J. H., HERSONSKY, S. & VESELOV, V., Real-oriented blow-ups and Hirzebruch-Inoue surfaces. In preparation.
37. HIRONAKA, H., Desingularization of complex-analytic varieties, in Actes du Congrès International de Mathématiciens, tome II (Nice, 1970), pp. 627-631. Gauthier-Villars, Paris, 1971.
38. - Triangulations of algebraic sets, in Algebraic Geometry (Arcata, CA, 1974), pp. 165 185. Proc. Sympos. Pure Math., 29. Amer. Math. Soc., Providence, RI, 1975.
39. - Triangulations of algebraic sets, in Algebraic Geometry (Arcata, CA, 1974), pp. 165 185. Proc. Sympos. Pure Math., 29. Amer. Math. Soc., Providence, RI, 1975.
40. HIRZEBRUCH, F., Hilbert modular surfaces. Enseign. Math. (2), 19 (1973), 183-281.
41. HIRZEBRUCH, F., NEUMANN, W. D. & KOH, S. S., Differentiable Manifolds and Quadratic Forms. Lecture Notes in Pure and Appl. Math., 4. Marcel Dekker, New York, 1971.
42. HOPF, H., Über die Abbildungen der 3-Sphäre auf die Kugelfläche. Math. Ann., 104 (1931), 637-665.
43. - Zur Topologie der komplexen Mannigfaltigkeiten, in Studies and Essays Presented to R. Courant on his 60th Birthday, pp. 167-185. Interscience, New York, 1948.
44. HUBBARD, J. H. & OBERSTE-VORTH, R. W., Hénon mappings in the complex domain, I: The global topology of dynamical space. Inst. Hautes Études Sci. Publ. Math., 79 (1994), 5 46.
45. - Hénon mappings in the complex domain, II: Projective and inductive limits of polynomials, in Real and Complex Dynamical Systems (Hillerød, 1993), pp. 89-132. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 464. Kluwer, Dordrecht, 1995.
46. - Hénon mappings in the complex domain, II: Projective and inductive limits of polynomials, in Real and Complex Dynamical Systems (Hillerød, 1993), pp. 89-132. NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 464. Kluwer, Dordrecht, 1995.
47. - Hénon mappings in the complex domain, III: The case of a single attracting fixed point. In preparation.
48. - The non-transversality invariant. Preprint, 1999.
49. n. Indiana Univ. Math. J., 43 (1994), 321-365.
50. 2 viewed as a global dynamical system. Preprint 2000/1, SUNY Stony Brook Institute for Mathematical Sciences.
51. - Newton's method in several variables. In preparation.
52. 2 as dynamical systems. Preprint 1997/11, SUNY Stony Brook Institute for Mathematical Sciences.
53. HUBBARD, J. H., The Hénon mapping in the complex domain, in Chaotic Dynamics and Fractals (Atlanta, GA, 1985), pp. 101-111. Notes Rep. Math. Sci. Engrg., 2. Academic Press, Orlando, FL, 1986.
54. HUBBARD, J. H., The Hénon mapping in the complex domain, in Chaotic Dynamics and Fractals (Atlanta, GA, 1985), pp. 101-111. Notes Rep. Math. Sci. Engrg., 2. Academic Press, Orlando, FL, 1986.
55. MILNOR, J., Topology from the Differentiable Viewpoint. The University Press of Virginia, Charlottesville, VA, 1965.
56. - Singular Points of Complex Hypersurfaces. Ann. of Math. Stud., 61. Princeton Univ. Press, Princeton, NJ, 1968.
57. - Nonexpansive Hénon maps. Adv. in Math., 69 (1988), 109-114.
58. - Personal communication, 1995.
59. ORLIK, P., Seifert Manifolds. Lecture Notes in Math., 291. Springer-Verlag, New York, 1972.
60. SHAFAREVIC, I. R., Algebraic Surfaces. Proc. Steklov Inst. Math., 75. Amer. Math. Soc., Providence, RI, 1965.
61. - Basic Algebraic Geometry, Vols. I and II. Springer-Verlag, Berlin, 1994.
62. 2. Ergodic Theory Dynamical Systems, 10 (1990), 823-827.
63. SPANIER, E., Algebraic Topology. McGraw-Hill, New York, 1966.
64. THURSTON, W. P., Three-Dimensional Geometry and Topology, Vol. 1. Princeton Math. Ser., 35. Princeton Univ. Press, Princeton, NJ, 1997.
65. VESELOV, V., A compactification of the Fatou mapping as a dynamical system. Thesis, University of South Florida, 1996.