Polynomial diffeomorphisms of C 2 : VII. Hyperbolicity and external rays
Bedford, Eric ; Smillie, John
Annales scientifiques de l'École Normale Supérieure, Tome 32 (1999), p. 455-497 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{ASENS_1999_4_32_4_455_0,
     author = {Bedford, Eric and Smillie, John},
     title = {Polynomial diffeomorphisms of $C^2$ : VII. Hyperbolicity and external rays},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {32},
     year = {1999},
     pages = {455-497},
     doi = {10.1016/s0012-9593(99)80020-2},
     mrnumber = {2000h:32021},
     zbl = {0952.37008},
     mrnumber = {1693587},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1999_4_32_4_455_0}
}

Bedford, Eric; Smillie, John. Polynomial diffeomorphisms of $C^2$ : VII. Hyperbolicity and external rays. Annales scientifiques de l'École Normale Supérieure, Tome 32 (1999) pp. 455-497. doi : 10.1016/s0012-9593(99)80020-2. http://gdmltest.u-ga.fr/item/ASENS_1999_4_32_4_455_0/

[BLS] E. Bedford, M. Lyubich and J. Smillie, Polynomial diffeomorphims of C2. IV : The measure of maximal entropy and laminar currents, Invent. math., 112, 1993, pp. 77-125. | MR 94g:32035 | Zbl 0792.58034

[BS1] E. Bedford and J. Smillie, Polynomial diffeomorphisms of C2 : Currents, equilibrium measure and hyperbolicity, Invent. Math., 87, 1990, pp. 69-99. | MR 92a:32035 | Zbl 0721.58037

[BS2] E. Bedford and J. Smillie, Polynomial diffeomorphisms of C2 II : Stable manifolds and recurrence, Journal of the AMS 4, 1991, pp. 657-679. | MR 92m:32048 | Zbl 0744.58068

[BS5] E. Bedford and J. Smillie, Polynomial diffeomorphisms of C2 V : Critical points and Lyapunov exponents, J. of Geometric Analysis, to appear. | Zbl 1004.37027

[BS6] E. Bedford and J. Smillie, Polynomial diffeomorphisms of C2 VI : Connectivity of J, Annals of Math., 148, 1998, pp. 1-41. | MR 2000b:32040 | Zbl 0916.58022

[BS] E. Bedford and J. Smillie, External rays in the dynamics of polynomial automorphisms of C2, in : Complex Geometric Analysis in Pohang, K.-T. Kim and S.G. Krantz, eds. Contemporary Math., 1998.

[B] G. Buzzard, Persistent homoclinic tangencies and infinitely many sinks for automorphisms of C2, PhD Thesis, U. of Michigan, 1995.

[C] A. Candel, Uniformization of surface laminations, Ann. scient. Éc. Norm. Sup., 26, 1993, pp. 489-516. | Numdam | MR 94f:57025 | Zbl 0785.57009

[DH] A. Douady and J. Hubbard, Itération des polynômes quadratiques complexes, C.R. Acad. Sc. Paris, t. 294, 1982, pp. 123-126. | MR 83m:58046 | Zbl 0483.30014

[F] D. Fried, Finitely presented dynamical systems, Ergod. Th. & Dynam. Sys., 7, 1987, pp. 489-507. | MR 89h:58157 | Zbl 0652.54028

[FM] S. Friedland and J. Milnor, Dynamical properties of plane polynomial automorphisms, Ergod. Th. & Dynam. Sys., 9, 1989, pp. 67-99. | MR 90f:58163 | Zbl 0651.58027

[G] E. Ghys, Holomorphic Anosov systems, Inventiones math., 119, 1995, pp. 585-614. | MR 95k:58116 | Zbl 0831.58041

[H] J.H. Hubbard, Hénon mappings in the complex domain, in : Chaotic Dynamics and Fractals, ed. M. Barnsley & S. Demko, Academic Press, 1986, pp. 101-111. | MR 858009 | Zbl 0601.32029

[HO1] J.H. Hubbard and R. Oberste-Vorth, Hénon mappings in the complex domain I : The global topology of dynamical space, Inst. Hautes Études Sci. Publ. Math., 79, 1994, pp. 5-46. | Numdam | MR 96a:58157 | Zbl 0839.54029

[HO2] J.H. Hubbard and R. Oberste-Vorth, Hénon mappings in the complex domain II : Projective and inductive limits of polynomials, in : Real and Complex Dynamical Systems, B. Branner and P. Hjorth, eds., 1995, pp. 89-132. | MR 96h:58147 | Zbl 0874.54037

[MSS] R. Mané, P. Sad and D. Sullivan, On the dynamics of rational maps, Ann. scient. Éc. Norm. Sup., 16, 1983, pp. 193-217. | Numdam | MR 85j:58089 | Zbl 0524.58025

[MS] C. Moore and C. Schochet, Global Analysis of Foliated Spaces, Springer-Verlag, New York, 1988. | MR 89h:58184 | Zbl 0648.58034

[NV] R. Näkki and J. Väisälä, John disks, Exposition. Math., 9, 1991, pp. 3-43. | MR 92i:30021 | Zbl 0757.30028

[O] R. Oliva, On the combinatorics of external rays in the dynamics of the complex Hénon map, PhD Thesis, Cornell University, 1998.

[P] D. Pixton, Markov neighborhoods for zero-dimensional basic sets, Trans. AMS, 279, 1983, pp. 431-462. | MR 85c:58062 | Zbl 0528.58023