Holomorphic dynamics and renormalization : a volume in honour of John Milnor's 75th birthday
著者
書誌事項
Holomorphic dynamics and renormalization : a volume in honour of John Milnor's 75th birthday
（Fields Institute communications, 53）
American Mathematical Society, 2008
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注記
At head of title: The Fields Institute for Research in Mathematical Sciences
Proceedings of a workshop held on Mar. 7-11, 2006
Includes bibliographical references
内容説明・目次
内容説明
The papers collected in this volume reflect some of the directions of research in two closely related fields: Complex Dynamics and Renormalization in Dynamical Systems. While dynamics of polynomial mappings, particularly quadratics, has by now reached a mature state of development, much less is known about non-polynomial rational maps. The reader will be introduced into this fascinating world and a related area of transcendental dynamics by the papers in this volume. A graduate student will find an area rich with open problems and beautiful computer simulations. A survey by V. Nekrashevych introduces the reader to iterated monodromy groups of rational mappings, a recently developed subject that links geometric group theory to combinatorics of rational maps.In this new language, many questions related to Thurston's theory of branched coverings of the sphere can be answered explicitly. Renormalization theory occupies a central place in modern Complex Dynamics. The progress in understanding the structure of the Mandelbrot set, polynomial Julia sets, and Feigenbaum-type universalities stems from renormalization techniques. Renormalization of circle maps and rotation domains, such as Siegel disks, can be understood in the context of the classical KAM theory. Corresponding phenomena in higher dimensions, such as universal scaling in area-preserving maps in 2D, on the boundary of KAM, pose a challenging problem. A survey by H. Koch and several other papers in the volume will introduce the reader to this direction of study.
目次
Schwarzian derivatives and cylinder maps by A. Bonifant and J. Milnor Holomorphic dynamics: Symbolic dynamics and self-similar groups by V. Nekrashevych Are there critical points on the boundaries of mother hedgehogs? by D. K. Childers Finiteness for degenerate polynomials by L. DeMarco Cantor webs in the parameter and dynamical planes of rational maps by R. L. Devaney Simple proofs of uniformization theorems by A. A. Glutsyuk The Yoccoz combinatorial analytic invariant by C. L. Petersen and P. Roesch Bifurcation loci of exponential maps and quadratic polynomials: Local connectivity, triviality of fibers, and density of hyperbolicity by L. Rempe and D. Schleicher Rational and transcendental Newton maps by J. Ruckert Newton's method as a dynamical system: Efficient root finding of polynomials and the Riemann $\zeta$ function by D. Schleicher The external boundary of $M_2$ by V. Timorin Renormalization: Renormalization of vector fields by H. Koch Renormalization of arbitrary weak noises for one-dimensional critical dynamical systems: Summary of results and numerical explorations by O. Diaz-Espinosa and R. de la Llave KAM for the nonlinear Schrodinger equation--A short presentation by H. L. Eliasson and S. B. Kuksin Siegel disks and renormalization fixed points by M. Yampolsky.
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