Описание: This text, the second of two volumes, builds on the foundational material on ergodic theory and geometric measure theory provided in Volume I, and applies all the techniques discussed to describe the beautiful and rich dynamics of elliptic functions. The text begins with an introduction to topological dynamics of transcendental meromorphic functions, before progressing to elliptic functions, discussing at length their classical properties, measurable dynamics and fractal geometry. The authors then look in depth at compactly non-recurrent elliptic functions. Much of this material is appearing for the first time in book or paper form. Both senior and junior researchers working in ergodic theory and dynamical systems will appreciate what is sure to be an indispensable reference.
Автор: A`Campo Norbert Название: Topological, Differential and Conformal Geometry of Surfaces ISBN: 3030890317 ISBN-13(EAN): 9783030890315 Издательство: Springer Рейтинг: Цена: 7685.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces.
Автор: Pollicott, Mark (university Of Manchester) Название: Open conformal systems and perturbations of transfer operators ISBN: 331972178X ISBN-13(EAN): 9783319721781 Издательство: Springer Рейтинг: Цена: 6288.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 1. Introduction.- 2. Singular Perturbations of Classical Original Perron-Frobenius Operators on Countable Alphabet Symbol Spaces.- 3. Symbol Escape Rates and the Survivor Set K(Un).- 4. Escape Rates for Conformal GDMSs and IFSs.- 5. Applications: Escape Rates for Multimodal Mapsand One-Dimensional Complex Dynamics.
The purpose of this monograph is two-fold: it introduces a conceptual language for the geometrical objects underlying Painleve equations, and it offers new results on a particular Painleve III equation of type PIII (D6), called PIII (0, 0, 4, -4), describing its relation to isomonodromic families of vector bundles on P1 with meromorphic connections. This equation is equivalent to the radial sine (or sinh) Gordon equation and, as such, it appears widely in geometry and physics. It is used here as a very concrete and classical illustration of the modern theory of vector bundles with meromorphic connections.
Complex multi-valued solutions on C* are the natural context for most of the monograph, but in the last four chapters real solutions on R>0 (with or without singularities) are addressed. These provide examples of variations of TERP structures, which are related to tt∗ geometry and harmonic bundles.
As an application, a new global picture o0 is given.
Автор: Mariusz Urbanski, Mark Pollicott Название: Asymptotic Counting in Conformal Dynamical Systems ISBN: 1470465779 ISBN-13(EAN): 9781470465773 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 10659.00 р. Наличие на складе: Нет в наличии.
Описание: This Book Is Aimed At Graduate Students And Researchers In Physics And Mathematics Who Seek To Understand The Basics Of Supersymmetry From A Mathematical Point Of View. It Provides A Bridge Between The Physical And Mathematical Approaches To The Superworld. The Physicist Who Is Devoted To Learning The Basics Of Supergeometry Can Find A Friendly Approach Here, Since Only The Concepts That Are Strictly Necessary Are Introduced. On The Other Hand, The Mathematician Who Wants To Learn From Physics Will Find That All The Mathematical Assumptions Are Firmly Rooted In Physical Concepts. This May Open Up A Channel Of Communication Between The Two Communities Working On Different Aspects Of Supersymmetry. Starting From Special Relativity And Minkowski Space, The Idea Of Conformal Space And Superspace Is Built Step By Step In A Mathematically Rigorous Way, And Always Connecting With The Ideas And Notation Used In Physics. While The Book Is Mainly Devoted To These Important Physical Examples Of Superspaces, It Can Also Be Used As An Introduction To The Field Of Supergeometry, Where A Reader Can Ease Into The Subject Without Being Overwhelmed With The Technical Difficulties.
Автор: Beliaev Dmitry Название: Conformal Maps and Geometry ISBN: 1786346133 ISBN-13(EAN): 9781786346131 Издательство: World Scientific Publishing Рейтинг: Цена: 14256.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 'I very much enjoyed reading this book ... Each chapter comes with well thought-out exercises, solutions to which are given at the end of the chapter. Conformal Maps and Geometry presents key topics in geometric function theory and the theory of univalent functions, and also prepares the reader to progress to study the SLE. It succeeds admirably on both counts.'MathSciNetGeometric function theory is one of the most interesting parts of complex analysis, an area that has become increasingly relevant as a key feature in the theory of Schramm-Loewner evolution.Though Riemann mapping theorem is frequently explored, there are few texts that discuss general theory of univalent maps, conformal invariants, and Loewner evolution. This textbook provides an accessible foundation of the theory of conformal maps and their connections with geometry.It offers a unique view of the field, as it is one of the first to discuss general theory of univalent maps at a graduate level, while introducing more complex theories of conformal invariants and extremal lengths. Conformal Maps and Geometry is an ideal resource for graduate courses in Complex Analysis or as an analytic prerequisite to study the theory of Schramm-Loewner evolution.
Описание: This book gives an authoritative treatment of the Verlinde formula for the dimension of conformal blocks, including a complete proof and the connection to generalized theta functions. It will be of interest to senior graduate students and researchers in geometry, representation theory and theoretical physics.
This book consists of three volumes. The first volume contains introductory accounts of topological dynamical systems, fi nite-state symbolic dynamics, distance expanding maps, and ergodic theory of metric dynamical systems acting on probability measure spaces, including metric entropy theory of Kolmogorov and Sinai. More advanced topics comprise infi nite ergodic theory, general thermodynamic formalism, topological entropy and pressure. Thermodynamic formalism of distance expanding maps and countable-alphabet subshifts of fi nite type, graph directed Markov systems, conformal expanding repellers, and Lasota-Yorke maps are treated in the second volume, which also contains a chapter on fractal geometry and its applications to conformal systems. Multifractal analysis and real analyticity of pressure are also covered. The third volume is devoted to the study of dynamics, ergodic theory, thermodynamic formalism and fractal geometry of rational functions of the Riemann sphere.
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