Dynamics of shift-like polynomial diffeomorphisms of $\textbf {C}^N$
Authors:
Eric Bedford and Victoria Pambuccian
Journal:
Conform. Geom. Dyn. 2 (1998), 45-55
MSC (1991):
Primary 32H50
DOI:
https://doi.org/10.1090/S1088-4173-98-00027-7
Published electronically:
May 12, 1998
MathSciNet review:
1624646
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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 ${\mathbf C}^2$.
- Eric Bedford and John Smillie, Polynomial diffeomorphisms of ${\bf C}^2$: currents, equilibrium measure and hyperbolicity, Invent. Math. 103 (1991), no. 1, 69–99. MR 1079840, DOI https://doi.org/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 https://doi.org/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 ${\bf C}^2$ and Fatou-Bieberbach domains, Duke Math. J. 65 (1992), no. 2, 345–380. MR 1150591, DOI https://doi.org/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 https://doi.org/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 ${\bf C}^n$, Indiana Univ. Math. J. 43 (1994), no. 1, 321–365. MR 1275463, DOI https://doi.org/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
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Additional Information
Eric Bedford
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email:
bedford@indiana.edu
Victoria Pambuccian
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Address at time of publication:
Department of Mathematics, SUNY Potsdam, Potsdam, New York 13676
Email:
pambucv@potsdam.edu
Received by editor(s):
January 5, 1998
Received by editor(s) in revised form:
March 16, 1998
Published electronically:
May 12, 1998
Article copyright:
© Copyright 1998
American Mathematical Society
