Dynamics of horizontal-like maps in higher dimension

2007/10/22 by Dinh, T. -C., Nguyen, V. -A., Sibony, N. · 1 citation
#32H50 (Secondary) #32U40 #37F (Primary) #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.0710.4007

Abstract

We study the regularity of the Green currents and of the equilibrium measure associated to a horizontal-like map in C^k, under a natural assumption on the dynamical degrees. We estimate the speed of convergence towards the Green currents, the decay of correlations for the equilibrium measure and the Lyapounov exponents. We show in particular that the equilibrium measure is hyperbolic. We also show that the Green currents are the unique invariant vertical and horizontal positive closed currents. The results apply, in particular, to Henon-like maps, to regular polynomial automorphisms of C^k and to their small pertubations.

Cited by

• log-Hölder regularity of currents and equidistribution towards Green currents

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