Dynamics of shift-like polynomial diffeomorphisms of 𝐶^{𝑁}

Bedford, Eric; Pambuccian, Victoria

doi:10.1090/S1088-4173-98-00027-7

Dynamics of shift-like polynomial diffeomorphisms of $\textbf {C}^N$
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by Eric Bedford and Victoria Pambuccian

Conform. Geom. Dyn. 2 (1998), 45-55

DOI: https://doi.org/10.1090/S1088-4173-98-00027-7

Published electronically: May 12, 1998

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Abstract:

We identify a family of polynomial diffeomorphisms of ${\mathbf C}^N$ and show that these mappings may be studied using certain methods (filtration and potential-theoretic) which were developed for the study of polynomial diffeomorphisms of ${\mathbf C}^2$.

References

Eric Bedford and John Smillie, Polynomial diffeomorphisms of $\textbf {C}^2$: currents, equilibrium measure and hyperbolicity, Invent. Math. 103 (1991), no. 1, 69–99. MR 1079840, DOI 10.1007/BF01239509
Eric Bedford and B. A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation, Invent. Math. 37 (1976), no. 1, 1–44. MR 445006, DOI 10.1007/BF01418826
G. Buzzard and J. Smillie, Complex dynamics in several variables, Flavors of Geometry, MSRI Publications, Vol. 31, 1997.
John Erik Fornæss and Nessim Sibony, Complex Hénon mappings in $\textbf {C}^2$ and Fatou-Bieberbach domains, Duke Math. J. 65 (1992), no. 2, 345–380. MR 1150591, DOI 10.1215/S0012-7094-92-06515-X
Shmuel Friedland and John Milnor, Dynamical properties of plane polynomial automorphisms, Ergodic Theory Dynam. Systems 9 (1989), no. 1, 67–99. MR 991490, DOI 10.1017/S014338570000482X
J.H. Hubbard, 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.
John H. Hubbard and Peter Papadopol, Superattractive fixed points in $\textbf {C}^n$, Indiana Univ. Math. J. 43 (1994), no. 1, 321–365. MR 1275463, DOI 10.1512/iumj.1994.43.43014
Maciej Klimek, Pluripotential theory, London Mathematical Society Monographs. New Series, vol. 6, The Clarendon Press, Oxford University Press, New York, 1991. Oxford Science Publications. MR 1150978