Complex Dynamics and Renormalization
Complex Dynamics and Renormalization
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发表时间：
1994-11
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通讯作者：
C. McMullen
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作者：
C. McMullen
解决研究人员和研究生在分析，几何和动力学的积极会议场地，这本书提出了二次多项式的重整化的研究和复杂动力学技术的快速介绍。它的中心问题是无限重正化的二次多项式f（z）= z2 + c的结构。正如费根鲍姆所发现的那样，这样的映射在无限多个尺度上表现出形式的重复。利用双曲几何中的普遍估计，本文给出了可能出现的极限形式的分析，并为多项式f建立了一个刚性准则。这一准则支持了关于有理映射的行为和Mandelbrot集的结构的一般命题。主要论证的过程涉及现代复杂动力学的许多方面。包括在几何函数理论，拟共形映射和双曲几何的基础结果。大多数的工具都讨论了一般多项式和有理映射的设置。
Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set.The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.