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]**David E. Barrett, Eric Bedford, and Jiri Dadok,*𝑇ⁿ-actions on holomorphically separable complex manifolds*, Math. Z.**202**(1989), no. 1, 65–82. MR**1007740**, https://doi.org/10.1007/BF01180684**[B]**Eric Bedford,*On the automorphism group of a Stein manifold*, Math. Ann.**266**(1983), no. 2, 215–227. MR**724738**, https://doi.org/10.1007/BF01458443**[BS1]**Eric Bedford and John Smillie,*Polynomial diffeomorphisms of 𝐶²: currents, equilibrium measure and hyperbolicity*, Invent. Math.**103**(1991), no. 1, 69–99. MR**1079840**, https://doi.org/10.1007/BF01239509**[BS2]**Eric Bedford and John Smillie,*Fatou-Bieberbach domains arising from polynomial automorphisms*, Indiana Univ. Math. J.**40**(1991), no. 2, 789–792. MR**1119197**, https://doi.org/10.1512/iumj.1991.40.40035**[Bi]**B. Bielefeld,*Conformal dynamics problem list*, SUNY Stony Brook Institute for Mathematical Sciences, preprint, 1990.**[FM]**Shmuel Friedland and John Milnor,*Dynamical properties of plane polynomial automorphisms*, Ergodic Theory Dynam. Systems**9**(1989), no. 1, 67–99. MR**991490**, https://doi.org/10.1017/S014338570000482X**[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]**Lars Hörmander,*An introduction to complex analysis in several variables*, 3rd ed., North-Holland Mathematical Library, vol. 7, North-Holland Publishing Co., Amsterdam, 1990. MR**1045639****[HO]**J. H. Hubbard and R. Oberste-Vorth,*Hénon mappings in the complex domain*, in preparation.**[K]**Anatole Katok,*Nonuniform hyperbolicity and structure of smooth dynamical systems*, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983) PWN, Warsaw, 1984, pp. 1245–1253. MR**804774****[N]**Sheldon E. Newhouse,*The creation of nontrivial recurrence in the dynamics of diffeomorphisms*, Chaotic behavior of deterministic systems (Les Houches, 1981) North-Holland, Amsterdam, 1983, pp. 381–442. MR**724468****[RR]**Jean-Pierre Rosay and Walter Rudin,*Holomorphic maps from 𝐶ⁿ to 𝐶ⁿ*, Trans. Amer. Math. Soc.**310**(1988), no. 1, 47–86. MR**929658**, https://doi.org/10.1090/S0002-9947-1988-0929658-4**[S]**John Smillie,*The entropy of polynomial diffeomorphisms of 𝐶²*, Ergodic Theory Dynam. Systems**10**(1990), no. 4, 823–827. MR**1091429**, https://doi.org/10.1017/S0143385700005927**[Z]**Eduard Zehnder,*A simple proof of a generalization of a theorem by C. L. Siegel*, Geometry and topology (Proc. III Latin Amer. School of Math., Inst. Mat. Pura Aplicada CNPq, Rio de Janeiro, 1976) Springer, Berlin, 1977, pp. 855–866. Lecture Notes in Math., Vol. 597. MR**0461575**

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

Article copyright:
© Copyright 1991
American Mathematical Society