Polynomial diffeomorphisms of C 2 : VII. Hyperbolicity and external rays

Eric Bedford; John Smillie

Annales scientifiques de l'École Normale Supérieure (1999)

  • Volume: 32, Issue: 4, page 455-497
  • ISSN: 0012-9593

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Bedford, Eric, and Smillie, John. "Polynomial diffeomorphisms of $C^2$ : VII. Hyperbolicity and external rays." Annales scientifiques de l'École Normale Supérieure 32.4 (1999): 455-497. <http://eudml.org/doc/82494>.

@article{Bedford1999,
author = {Bedford, Eric, Smillie, John},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {polynomial diffeomorphisms; dynamics; Julia set; external rays; solenoid; pinch points},
language = {eng},
number = {4},
pages = {455-497},
publisher = {Elsevier},
title = {Polynomial diffeomorphisms of $C^2$ : VII. Hyperbolicity and external rays},
url = {http://eudml.org/doc/82494},
volume = {32},
year = {1999},
}

TY - JOUR
AU - Bedford, Eric
AU - Smillie, John
TI - Polynomial diffeomorphisms of $C^2$ : VII. Hyperbolicity and external rays
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1999
PB - Elsevier
VL - 32
IS - 4
SP - 455
EP - 497
LA - eng
KW - polynomial diffeomorphisms; dynamics; Julia set; external rays; solenoid; pinch points
UR - http://eudml.org/doc/82494
ER -

References

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  1. [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. Zbl0792.58034MR94g:32035
  2. [BS1] E. BEDFORD and J. SMILLIE, Polynomial diffeomorphisms of C2 : Currents, equilibrium measure and hyperbolicity, Invent. Math., 87, 1990, pp. 69-99. Zbl0721.58037MR92a:32035
  3. [BS2] E. BEDFORD and J. SMILLIE, Polynomial diffeomorphisms of C2 II : Stable manifolds and recurrence, Journal of the AMS 4, 1991, pp. 657-679. Zbl0744.58068MR92m:32048
  4. [BS5] E. BEDFORD and J. SMILLIE, Polynomial diffeomorphisms of C2 V : Critical points and Lyapunov exponents, J. of Geometric Analysis, to appear. Zbl1004.37027
  5. [BS6] E. BEDFORD and J. SMILLIE, Polynomial diffeomorphisms of C2 VI : Connectivity of J, Annals of Math., 148, 1998, pp. 1-41. Zbl0916.58022MR2000b:32040
  6. [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. 
  7. [B] G. BUZZARD, Persistent homoclinic tangencies and infinitely many sinks for automorphisms of C2, PhD Thesis, U. of Michigan, 1995. 
  8. [C] A. CANDEL, Uniformization of surface laminations, Ann. scient. Éc. Norm. Sup., 26, 1993, pp. 489-516. Zbl0785.57009MR94f:57025
  9. [DH] A. DOUADY and J. HUBBARD, Itération des polynômes quadratiques complexes, C.R. Acad. Sc. Paris, t. 294, 1982, pp. 123-126. Zbl0483.30014MR83m:58046
  10. [F] D. FRIED, Finitely presented dynamical systems, Ergod. Th. & Dynam. Sys., 7, 1987, pp. 489-507. Zbl0652.54028MR89h:58157
  11. [FM] S. FRIEDLAND and J. MILNOR, Dynamical properties of plane polynomial automorphisms, Ergod. Th. & Dynam. Sys., 9, 1989, pp. 67-99. Zbl0651.58027MR90f:58163
  12. [G] E. GHYS, Holomorphic Anosov systems, Inventiones math., 119, 1995, pp. 585-614. Zbl0831.58041MR95k:58116
  13. [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. Zbl0601.32029MR858009
  14. [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. Zbl0839.54029MR96a:58157
  15. [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. Zbl0874.54037MR96h:58147
  16. [MSS] R. MANÉ, P. SAD and D. SULLIVAN, On the dynamics of rational maps, Ann. scient. Éc. Norm. Sup., 16, 1983, pp. 193-217. Zbl0524.58025MR85j:58089
  17. [MS] C. MOORE and C. SCHOCHET, Global Analysis of Foliated Spaces, Springer-Verlag, New York, 1988. Zbl0648.58034MR89h:58184
  18. [NV] R. NÄKKI and J. VÄISÄLÄ, John disks, Exposition. Math., 9, 1991, pp. 3-43. Zbl0757.30028MR92i:30021
  19. [O] R. OLIVA, On the combinatorics of external rays in the dynamics of the complex Hénon map, PhD Thesis, Cornell University, 1998. 
  20. [P] D. PIXTON, Markov neighborhoods for zero-dimensional basic sets, Trans. AMS, 279, 1983, pp. 431-462. Zbl0528.58023MR85c:58062

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