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Continuity of Lyapunov exponents for polynomial automorphisms of $\mathbb{C}^2$

Published online by Cambridge University Press:  03 May 2007

ROMAIN DUJARDIN
ROMAIN DUJARDIN
Affiliation:
Université Paris 7 et Institut de Mathématiques de Jussieu, Équipe Géométrie et Dynamique, Case 7012, 2 place Jussieu, 75251 Paris Cedex 05, France (e-mail: dujardin@math.jussieu.fr)
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Abstract

We prove two continuity theorems for the Lyapunov exponents of the maximal entropy measure of polynomial automorphisms of $\mathbb{C}^2$. The first continuity result holds for any family of polynomial automorphisms of constant dynamical degree. The second result is the continuity of the upper exponent for families degenerating to a one-dimensional map.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 4 , August 2007 , pp. 1111 - 1133
Copyright
2007 Cambridge University Press

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