Polynomial diffeomorphisms of . II. Stable manifolds and recurrence

Authors:
Eric Bedford and John Smillie

Journal:
J. Amer. Math. Soc. **4** (1991), 657-679

MSC:
Primary 32H50; Secondary 32C30, 54H20, 58F23

DOI:
https://doi.org/10.1090/S0894-0347-1991-1115786-3

MathSciNet review:
1115786

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References | Similar Articles | Additional Information

**[BBD]**D. Barret, E. Bedford, and J. Dadok,*-actions on holomorphically separable complex manifolds*, Math. Z.**202**(1989), 65-82. MR**1007740 (90k:32003)****[B]**E. Bedford,*On the automorphism group of a Stein manifold*, Math. Ann.**266**(1983), 215-227. MR**724738 (85h:32049)****[BS1]**E. Bedford and J. Smillie,*Polynomial diffeomorphisms of*:*currents, equilibrium measure and hyperbolicity*, Invent. Math.**103**(1991), 69-99. MR**1079840 (92a:32035)****[BS2]**-,*Fatou-Bieberbach domains arising from polynomial automorphisms*, Indiana U. Math. J.**40**(1991), 789-792. MR**1119197 (92k:32044)****[Bi]**B. Bielefeld,*Conformal dynamics problem list*, SUNY Stony Brook Institute for Mathematical Sciences, preprint, 1990.**[FM]**S. Friedland and J. Milnor, Dynamical properties of plane polynomial automorphisms, Ergodic Theory Dynamical Systems**9**(1989), 67-99. MR**991490 (90f:58163)****[H]**M. Herman,*Recent results and some open questions on Siegel's linearization theorem of germs of complex analytic diffeomorphisms of**near a fixed point*, VIIIth International Congress on Mathematical Physics (Marseille, 1986), World Scientific Publ. Singapore, 1987, pp. 138-184.**[Ho]**L. Hörmander,*An introduction to complex analysis in several variables*, North-Holland, 1973. MR**1045639 (91a:32001)****[HO]**J. H. Hubbard and R. Oberste-Vorth,*Hénon mappings in the complex domain*, in preparation.**[K]**A. Katok,*Nonuniform hyperbolicity and structure of smooth dynamical systems*, Proc. Internat. Congr. Math., Warsaw, 1983. MR**804774 (87h:58173)****[N]**S. Newhouse,*The creation of non-trivial recurrence in the dynamics of diffeomorphisms*, Les Houches session XXXVI, Chaotic Behavior of Deterministic Systems (G. Iooss et al., eds.), North-Holland, 1983, pp. 381-442. MR**724468 (85d:58047)****[RR]**J.-P. Rosay and W. Rudin,*Holomorphic maps from*to , Trans. Amer. Math. Soc.**310**(1988), 47-86. MR**929658 (89d:32058)****[S]**J. Smillie,*The entropy of polynomial diffeomorphisms of*, Ergodic Theory Dynamical Systems (to appear). MR**1091429 (92b:58131)****[Z]**E. Zehnder,*A simple proof of a generalization of a Theorem by C. L. Siegel*, Geometry and Topology (J. Palis and M. do Carmo, eds.), Lecture Notes in Math., vol. 597, Springer-Verlag, New York, 1977, pp. 855-866. MR**0461575 (57:1560)**

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Additional Information

DOI:
https://doi.org/10.1090/S0894-0347-1991-1115786-3

Article copyright:
© Copyright 1991
American Mathematical Society