Complex Hyperbolic Kleinian Groups
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Complex Kleinian Groups
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Author : Angel Cano
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-05
Complex Kleinian Groups written by Angel Cano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-05 with Mathematics categories.
This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can be regarded too as being groups of holomorphic automorphisms of the complex projective line CP1. When going into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere?, or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories are different in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition. In the second case we are talking about an area of mathematics that still is in its childhood, and this is the focus of study in this monograph. This brings together several important areas of mathematics, as for instance classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and the uniformization problem for complex manifolds.
Hyperbolic Manifolds And Kleinian Groups
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Author : Katsuhiko Matsuzaki
language : en
Publisher: Clarendon Press
Release Date : 1998-04-30
Hyperbolic Manifolds And Kleinian Groups written by Katsuhiko Matsuzaki and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-04-30 with Mathematics categories.
A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, which is also regarded as a subgroup of Möbius transformations in the complex plane. The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex analysis. After 1960, Ahlfors and Bers were the leading researchers of Kleinian groups and helped it to become an active area of complex analysis as a branch of Teichmüller theory. Later, Thurston brought a revolution to this area with his profound investigation of hyperbolic manifolds, and at the same time complex dynamical approach was strongly developed by Sullivan. This book provides fundamental results and important theorems which are needed for access to the frontiers of the theory from a modern viewpoint.
Conformal Graph Directed Markov Systems On Carnot Groups
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Author : Vasileios Chousionis
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Conformal Graph Directed Markov Systems On Carnot Groups written by Vasileios Chousionis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
The authors develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, they develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter. They illustrate their results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.
Geometry And Dynamics Of Groups And Spaces
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Author : Mikhail Kapranov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-05
Geometry And Dynamics Of Groups And Spaces written by Mikhail Kapranov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-05 with Mathematics categories.
Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.
Complex Hyperbolic Kleinian Groups
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Author : William Mark Goldman
language : en
Publisher:
Release Date : 1991
Complex Hyperbolic Kleinian Groups written by William Mark Goldman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Kleinian groups categories.
Abstract: "Complex hyperbolic manifolds furnish the simplest examples of: (i) negatively curved Kähler manifolds and (ii) negatively curved Riemannian manifolds not having constant curvature. Their central importance is underscored by their appearance as the prototype of moduli spaces of various kinds of geometric structures. This paper surveys an ongoing project to find examples of complex hyperbolic manifolds by direct geometric construction of their fundamental groups. In particular complex hyperbolic Kleinian groups display both flexibility and rigidity -- compared, respectively, with their real and quaternionic counterparts. Deformations of Fuchsian groups as complex hyperbolic Kleinian groups are discussed."
Geometry Of Riemann Surfaces
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Author : William J. Harvey
language : en
Publisher: Cambridge University Press
Release Date : 2010-02-11
Geometry Of Riemann Surfaces written by William J. Harvey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-11 with Mathematics categories.
Original research and expert surveys on Riemann surfaces.
In The Tradition Of Thurston Ii
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Author : Ken’ichi Ohshika
language : en
Publisher: Springer Nature
Release Date : 2022-08-02
In The Tradition Of Thurston Ii written by Ken’ichi Ohshika and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-02 with Mathematics categories.
The purpose of this volume and of the other volumes in the same series is to provide a collection of surveys that allows the reader to learn the important aspects of William Thurston’s heritage. Thurston’s ideas have altered the course of twentieth century mathematics, and they continue to have a significant influence on succeeding generations of mathematicians. The topics covered in the present volume include com-plex hyperbolic Kleinian groups, Möbius structures, hyperbolic ends, cone 3-manifolds, Thurston’s norm, surgeries in representation varieties, triangulations, spaces of polygo-nal decompositions and of singular flat structures on surfaces, combination theorems in the theories of Kleinian groups, hyperbolic groups and holomorphic dynamics, the dynamics and iteration of rational maps, automatic groups, and the combinatorics of right-angled Artin groups.
Dynamical Systems Proceedings Of The International Conference In Honor Of Professor Liao Shantao
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Author : Lan Wen
language : en
Publisher: World Scientific
Release Date : 1999-12-16
Dynamical Systems Proceedings Of The International Conference In Honor Of Professor Liao Shantao written by Lan Wen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-16 with categories.
This volume constitutes the proceedings of the International Conference on Dynamical Systems in Honor of Prof. Liao Shantao (1920-97). The Third World Academy of Sciences awarded the first ever mathematics prize in 1985 to Prof. Liao in recognition of his foundational work in differentiable dynamical systems and his work in periodic transformation of spheres. The conference was held in Beijing in August 1998. There were about 90 participants, and nearly 60 talks were delivered.The topics covered include differentiable dynamics, topological dynamics, hamiltonian dynamics, complex dynamics, ergodic and stochastic dynamics, and fractals theory. Dynamical systems is a field with many difficult problems, and techniques are being developed to deal with those problems. This volume contains original studies of great mathematical depth and presents some of the fascinating numerical experiments.
Nonlinear Dynamics New Directions
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Author : Hernán González-Aguilar
language : en
Publisher: Springer
Release Date : 2015-03-09
Nonlinear Dynamics New Directions written by Hernán González-Aguilar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-09 with Technology & Engineering categories.
This book, along with its companion volume, Nonlinear Dynamics New Directions: Models and Applications, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Presents a rigorous treatment of fluctuations in dynamical systems and explores a range of topics in fractal analysis, among other fundamental topics · Features recent developments on large deviations for higher-dimensional maps, a study of measures resisting multifractal analysis and a overview of complex Kleninan groups · Includes thorough review of recent findings that emphasize new development prospects
The Proceedings Of The Conference S On Geometric Structures On Manifolds
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Author : Suhyoung Choi
language : en
Publisher:
Release Date : 1999
The Proceedings Of The Conference S On Geometric Structures On Manifolds written by Suhyoung Choi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Gauge fields (Physics) categories.