论文标题
$ \ mathbb {p}^k $ i的内态性的平衡状态：存在和属性
Equilibrium states of endomorphisms of $\mathbb{P}^k$ I: existence and properties
论文作者
论文摘要
我们开发了一种基于多功能理论的新方法，以研究$ \ mathbb p^k = \ mathbb p^k（\ mathbb c）$ y Mathbb p^k = \ mathbb c）$ y holomororphic nodormorphismist诱导的转移（Perron-frobenius）运算符。这种方法使我们能够证明平衡状态的存在和独特性和非常笼统的权重（由于dimension 1中的Denker-przytyckibavenski，在较高的较高的连续权重的情况下，在较高的维度中，在较高的尺寸中，在较高的尺寸中的denker-przytyckibański和Urbański-Zdunik。我们建立了平衡状态的许多属性，包括混合，混合，所有订单的混合以及排斥周期点的等分分配。我们的分析方法取代了对逆分支上的所有失真估计，具有独特的全局，动态电流的估计，使我们能够将动态问题减少到电流及其电位之间的比较。
We develop a new method, based on pluripotential theory, to study the transfer (Perron-Frobenius) operator induced on $\mathbb P^k = \mathbb P^k (\mathbb C)$ by a holomorphic endomorphism and a suitable continuous weight. This method allows us to prove the existence and uniqueness of the equilibrium state and conformal measure for very general weights (due to Denker-Przytycki-Urbański in dimension 1 and Urbański-Zdunik in higher dimensions, both in the case of H\''older continuous weights). We establish a number of properties of the equilibrium states, including mixing, K-mixing, mixing of all orders, and an equidistribution of repelling periodic points. Our analytic method replaces all distortion estimates on inverse branches with a unique, global, estimate on dynamical currents, and allows us to reduce the dynamical questions to comparisons between currents and their potentials.
