论文标题
千古理论，几何测量理论，保形度量和椭圆函数的动力学
Ergodic Theory, Geometric Measure Theory, Conformal Measures and the Dynamics of Elliptic Functions
论文作者
论文摘要
我们书的最终目的是介绍从$ \ c $到$ \ oc $的椭圆函数的动态，千古理论和几何形状的统一方法。我们将椭圆形功能视为最规则的先验杂种功能。杆构成了此类功能的重要特征，但临界值集是有限的，其基本区域的椭圆函数是“相同的”。从某种意义上说，这是类似于理性函数的先验性异常功能的一类。另一方面，差异很大。在此介绍过程中，我们将介绍它们。为了全面涵盖椭圆函数的动力学和几何形状，我们进行了大量的准备。这是在本书的前两个部分中完成的：第1部分，“厄运理论与衡量标准”以及第2部分，“几何和保形度量”。我们打算尽可能地自我包含，我们在第〜3部分中使用第〜1部分和第2部分的所有主要结果，以及处理椭圆功能的部分。 This book can be thus treated as a fairly comprehensive account of dynamics, ergodic theory, and fractal geometry of elliptic functions but also as a reference book (with proofs) for many results of geometric measure theory, finite and infinite abstract ergodic theory, Young's towers, measure--theoretic Kolmogorov--Sinai entropy, thermodynamic formalism, geometric function theory (in particular Koebe's Distortion定理和Riemann-Hurwitz公式），各种形式的共形度量，共形图的马尔可夫系统和迭代功能系统，椭圆函数的经典一般理论以及先验性meromoromormormormorphic函数的拓扑动态。
The ultimate goal of our book is to present a unified approach to the dynamics, ergodic theory, and geometry of elliptic functions from $\C$ to $\oc$. We consider elliptic functions as a most regular class of transcendental meromorphic functions. Poles form an essential feature of such functions but the set of critical values is finite and an elliptic function is "the same" on its of its fundamental regions. In a sense this is the class of transcendental meromorphic functions which resembles rational functions most. On the other hand, the differences are huge. We will touch on them in the course of this introduction. In order to comprehensively cover the dynamics and geometry of elliptic functions we make large preparations. This is done in the first two parts of the book: Part 1, "Ergodic Theory and Measures" and Part 2,"Geometry and Conformal Measures". We intend our book to be as self contained as possible and we use essentially all major results of Part~1 and Part~2 in Part~3 and Part~4 dealing with elliptic functions. This book can be thus treated as a fairly comprehensive account of dynamics, ergodic theory, and fractal geometry of elliptic functions but also as a reference book (with proofs) for many results of geometric measure theory, finite and infinite abstract ergodic theory, Young's towers, measure--theoretic Kolmogorov--Sinai entropy, thermodynamic formalism, geometric function theory (in particular Koebe's Distortion Theorems and Riemann--Hurwitz Formulas), various kinds of conformal measures, conformal graph Directed Markov systems and iterated function systems, classical general theory of elliptic functions, and topological dynamics of transcendental meromorphic functions.
