Renormalization And Geometry In One-dimensional And Complex Dynamics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Renormalization And Geometry In One-dimensional And Complex Dynamics write by Yunping Jiang. This book was released on 1996-09-20. Renormalization And Geometry In One-dimensional And Complex Dynamics available in PDF, EPUB and Kindle. About one and a half decades ago, Feigenbaum observed that bifurcations, from simple dynamics to complicated ones, in a family of folding mappings like quadratic polynomials follow a universal rule (Coullet and Tresser did some similar observation independently). This observation opened a new way to understanding transition from nonchaotic systems to chaotic or turbulent system in fluid dynamics and many other areas. The renormalization was used to explain this observed universality. This research monograph is intended to bring the reader to the frontier of this active research area which is concerned with renormalization and rigidity in real and complex one-dimensional dynamics. The research work of the author in the past several years will be included in this book. Most recent results and techniques developed by Sullivan and others for an understanding of this universality as well as the most basic and important techniques in the study of real and complex one-dimensional dynamics will also be included here.
Renormalization and Geometry in One-dimensional and Complex Dynamics
Renormalization and Geometry in One-dimensional and Complex Dynamics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Renormalization and Geometry in One-dimensional and Complex Dynamics write by Yunping Jiang. This book was released on 1996. Renormalization and Geometry in One-dimensional and Complex Dynamics available in PDF, EPUB and Kindle. The book is intended to help under- and postgraduate students and young scientists in the correct application of NMR to the solution of physico-chemical problems concerning the study of equilibria in solution. The first part of the book (Chapters 1–3) is a trivium, but should enable a student to design and conduct simple physico-chemical NMR experiments. The following chapters give illustrative material on the physico-chemical applications of NMR of increasing complexity. These chapters include the problem of determination of equilibrium and rate constants in solution, the study of paramagnetism using NMR, the application of Dynamic NMR techniques and relaxation measurements. A multipurpose nonlinear regression program is supplied (on disc for PC) and is referred to throughout the book.
Renormalization and Geometry in One-dimensional Dynamics
Renormalization and Geometry in One-dimensional Dynamics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Renormalization and Geometry in One-dimensional Dynamics write by Yunping Jiang. This book was released on 1996. Renormalization and Geometry in One-dimensional Dynamics available in PDF, EPUB and Kindle.
Complex Dynamics and Renormalization (AM-135), Volume 135
Complex Dynamics and Renormalization (AM-135), Volume 135 - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Complex Dynamics and Renormalization (AM-135), Volume 135 write by Curtis T. McMullen. This book was released on 2016-03-02. Complex Dynamics and Renormalization (AM-135), Volume 135 available in PDF, EPUB and Kindle. 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.
Julia Sets and Complex Singularities of Free Energies
Julia Sets and Complex Singularities of Free Energies - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Julia Sets and Complex Singularities of Free Energies write by Jianyong Qiao. This book was released on 2015-02-06. Julia Sets and Complex Singularities of Free Energies available in PDF, EPUB and Kindle. The author studies a family of renormalization transformations of generalized diamond hierarchical Potts models through complex dynamical systems. He proves that the Julia set (unstable set) of a renormalization transformation, when it is treated as a complex dynamical system, is the set of complex singularities of the free energy in statistical mechanics. He gives a sufficient and necessary condition for the Julia sets to be disconnected. Furthermore, he proves that all Fatou components (components of the stable sets) of this family of renormalization transformations are Jordan domains with at most one exception which is completely invariant. In view of the problem in physics about the distribution of these complex singularities, the author proves here a new type of distribution: the set of these complex singularities in the real temperature domain could contain an interval. Finally, the author studies the boundary behavior of the first derivative and second derivative of the free energy on the Fatou component containing the infinity. He also gives an explicit value of the second order critical exponent of the free energy for almost every boundary point.
