Complex 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.
Complex Kleinian Groups
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Author : Springer
language : en
Publisher:
Release Date : 2012-11-07
Complex Kleinian Groups written by Springer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-07 with categories.
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 Groups And Dynamics
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Author : C. S. Aravinda
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-05-01
Geometry Groups And Dynamics written by C. S. Aravinda 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 2015-05-01 with Mathematics categories.
This volume contains the proceedings of the ICTS Program: Groups, Geometry and Dynamics, held December 3-16, 2012, at CEMS, Almora, India. The activity was an academic tribute to Ravi S. Kulkarni on his turning seventy. Articles included in this volume, both introductory and advanced surveys, represent the broad area of geometry that encompasses a large portion of group theory (finite or otherwise) and dynamics in its proximity. These areas have been influenced by Kulkarni's ideas and are closely related to his work and contribution.
Spaces Of Kleinian Groups
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Author : Yair N. Minsky
language : en
Publisher: Cambridge University Press
Release Date : 2006-06-19
Spaces Of Kleinian Groups written by Yair N. Minsky 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 2006-06-19 with Mathematics categories.
The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, the last few years having seen the resolution of many longstanding conjectures. This volume contains important expositions and original work by some of the main contributors on topics such as topology and geometry of 3-manifolds, curve complexes, classical Ahlfors-Bers theory, computer explorations and projective structures. Researchers in these and related areas will find much of interest here.
Laminations And Foliations In Dynamics Geometry And Topology
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Author : Mikhail Lyubich
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Laminations And Foliations In Dynamics Geometry And Topology written by Mikhail Lyubich 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 2001 with Mathematics categories.
This volume is based on a conference held at SUNY, Stony Brook (NY). The concepts of laminations and foliations appear in a diverse number of fields, such as topology, geometry, analytic differential equations, holomorphic dynamics, and renormalization theory. Although these areas have developed deep relations, each has developed distinct research fields with little interaction among practitioners. The conference brought together the diverse points of view of researchers from different areas. This book includes surveys and research papers reflecting the broad spectrum of themes presented at the event. Of particular interest are the articles by F. Bonahon, "Geodesic Laminations on Surfaces", and D. Gabai, "Three Lectures on Foliations and Laminations on 3-manifolds", which are based on minicourses that took place during the conference.
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
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."
Theory Of Functions Of A Complex Variable
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Author : Forsyth
language : en
Publisher:
Release Date : 1893
Theory Of Functions Of A Complex Variable written by Forsyth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1893 with categories.