高维类水平映射的动力学
Dynamics of horizontal-like maps in higher dimension
摘要：
在动力学度的自然假设下，我们研究了C^k中类水平映射的格林流和平衡测度的正则性。我们估计的速度收敛到绿色电流，衰减的相关性的平衡测度和Lyapounov指数。我们特别证明了平衡测度是双曲的。我们还证明了格林流是唯一不变的垂直和水平正闭合流。这些结果特别适用于Henon型映射、C^k的正则多项式自同构及其小扰动。
英文摘要：
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.
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