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Polynomial diffeomorphisms of C2: currents, equilibrium measure and hyperbolicity

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References

  • [Be] Bedford, E.: On the automorphism group of a Stein manifold. Math. Ann.266, 215–227 (1983)

    Google Scholar 

  • [BT1] Bedford, E., Taylor, B.A.: The Dirichlet problem for a complex Monge-Ampère equation. Invent. Math.37 1–44 (1976)

    Google Scholar 

  • [BT2] Bedford, E., Taylor, B.A.: Fine topology, Šilov boundary, and (dd c)n. J. Funct. Anal.72, 225–251 (1987)

    Google Scholar 

  • [BC] Benedicks, M., Carleson, L.: The dynamics of the Hénon map. Preprint

  • [Bo1] Bowen, R.: Markov partitions for axiom-A diffeomorphisms. Am. J. Math.92, 725–747 (1970)

    Google Scholar 

  • [Bo2] Bowen, R.: On Axiom A Diffeomorphisms. CBMS-NSF Reg. Conf. Ser. Appl. Math. 35 (1978)

  • [BM] Bowen, R., Marcus, B.: Unique ergodicity for horocycle foliations. Isr. J. Math.26, 43–67 (1977)

    Google Scholar 

  • [Br] Brolin, H.: Invariant sets under iteration of rational functions. Ark. Mat.6, 103–144 (1965)

    Google Scholar 

  • [F] Federer, H.: Geometric measure theory. Berlin-Heidelberg-New York: Springer 1969

    Google Scholar 

  • [FM] Friedland, S., Milnor, J.: Dynamical properties of plane polynomial automorphisms. Ergodic Theory Dyn. Syst.9, 67–99 (1989)

    Google Scholar 

  • [He] Hénon, M.: A two-dimensional mapping with a strange attractor. Commun. Math. Phys.50, 69–77 (1976)

    Google Scholar 

  • [H] Hubbard, J.H.: The Hénon mapping in the complex domain. In: Chaotic Dynamics and Fractals, Barnsley, M., Demko, S. (eds.), pp. 101–111. New York: Academic Press 1986

    Google Scholar 

  • [HO] Hubbard, J. H., Oberste-Vorth, R.: Hénon mappings in the complex domain

  • [L] Lelong, P.: Fonctions plurisousharmoniques et formes différentielles positives. New York-Paris: Gordon and Breach 1968

    Google Scholar 

  • [N] Newhouse, S.: Lectures on dynamical systems. In: Dynamical Systems, C.I.M.E. Lectures Bressanone, Italy, June 1978, (Progress in Mathematics, vol. 8). Boston: Birkhäuser 1980

    Google Scholar 

  • [NZ] Nguyen Thanh Van, Zériahi, A.: Familles de polynômes presque partout bornées. Bull. Sci. Math.197, 81–91 (1987)

    Google Scholar 

  • [RS] Ruelle, D., Sullivan, D.: Currents, flows, and diffeomorphisms. Topology14, 319–327 (1975)

    Google Scholar 

  • [S] Shub, M.: Global stability of mappings. Berlin-Heidelberg-New York: Springer 1987

    Google Scholar 

  • [Sm] Smillie, J.: The entropy of polynomial diffeomorphisms ofC 2. Ergodic Theory Dyn. Syst. (to appear)

  • [Su] Sullivan, D.: Cycles for the dynamical study of foliated manifolds and complex manifolds. Invent. Math.36, 225–255 (1976)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, 47405, Bloomington, IN, USA

    Eric Bedford

  2. Department of Mathematics, Cornell University, 14853, Ithaca, NY, USA

    John Smillie

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  1. Eric Bedford
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  2. John Smillie
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Oblatum 19-VI-1989 & 5-II-1990

Partially supported by NSF grant # DMS-8602020.

Partially supported by NSF grant # DMS-8803228

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Bedford, E., Smillie, J. Polynomial diffeomorphisms of C2: currents, equilibrium measure and hyperbolicity. Invent Math 103, 69–99 (1991). https://doi.org/10.1007/BF01239509

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