Download or read book Flows on Homogeneous Spaces written by L. Auslander and published by . This book was released on 1985 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Flows on homogeneous spaces written by Louis Auslander and published by . This book was released on 1966 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Flows on Homogeneous Spaces written by Louis Auslander and published by Princeton University Press. This book was released on 1963-05-21 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Flows on Homogeneous Spaces. (AM-53), Volume 53, will be forthcoming.
Download or read book Flows on Homogeneous Spaces AM 53 Volume 53 written by Louis Auslander and published by Princeton University Press. This book was released on 2016-03-02 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, Flows on Homogeneous Spaces. (AM-53), Volume 53, will be forthcoming.
Download or read book Flows on Homogeneous Spaces written by Louis Auslander and published by . This book was released on 1963 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces written by M. Bachir Bekka and published by Cambridge University Press. This book was released on 2000-05-11 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.
Download or read book A Panorama of Number Theory Or The View from Baker s Garden written by Gisbert Wüstholz and published by Cambridge University Press. This book was released on 2002-09-26 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a selection of high quality articles on number theory by leading figures.
Download or read book Dynamical Systems on Homogeneous Spaces written by Aleksandr N. Starkov and published by American Mathematical Soc.. This book was released on 2000 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: A homogeneous flow is a dynamical system generated by the action of a closed subgroup $H$ of a Lie group $G$ on a homogeneous space of $G$. The study of such systems is of great significance because they constitute an algebraic model for more general and more complicated systems. Also, there are abundant applications to other fields of mathematics, most notably to number theory. The present book gives an extensive survey of the subject. In the first chapter the author discusses ergodicity and mixing of homogeneous flows. The second chapter is focused on unipotent flows, for which substantial progress has been made during the last 10-15 years. The culmination of this progress was M. Ratner's celebrated proof of far-reaching conjectures of Raghunathan and Dani. The third chapter is devoted to the dynamics of nonunipotent flows. The final chapter discusses applications of homogeneous flows to number theory, mainly to the theory of Diophantine approximations. In particular, the author describes in detail the famous proof of the Oppenheim-Davenport conjecture using ergodic properties of homogeneous flows.
Download or read book Riemannian Manifolds and Homogeneous Geodesics written by Valerii Berestovskii and published by Springer Nature. This book was released on 2020-11-05 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both classical and modern results, some very recent, many of which are due to the authors. The main focus is on the class of Riemannian manifolds with homogeneous geodesics and on some of its important subclasses. To keep the exposition self-contained the book also includes useful general results not only on geodesic orbit manifolds, but also on smooth and Riemannian manifolds, Lie groups and Lie algebras, homogeneous Riemannian manifolds, and compact homogeneous Riemannian spaces. The intended audience is graduate students and researchers whose work involves differential geometry and transformation groups.
Download or read book Ratner s Theorems on Unipotent Flows written by Dave Witte Morris and published by University of Chicago Press. This book was released on 2005-08-15 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theorems of Berkeley mathematician Marina Ratner have guided key advances in the understanding of dynamical systems. Unipotent flows are well-behaved dynamical systems, and Ratner has shown that the closure of every orbit for such a flow is of a simple algebraic or geometric form. In Ratner's Theorems on Unipotent Flows, Dave Witte Morris provides both an elementary introduction to these theorems and an account of the proof of Ratner's measure classification theorem. A collection of lecture notes aimed at graduate students, the first four chapters of Ratner's Theorems on Unipotent Flows can be read independently. The first chapter, intended for a fairly general audience, provides an introduction with examples that illustrate the theorems, some of their applications, and the main ideas involved in the proof. In the following chapters, Morris introduces entropy, ergodic theory, and the theory of algebraic groups. The book concludes with a proof of the measure-theoretic version of Ratner's Theorem. With new material that has never before been published in book form, Ratner's Theorems on Unipotent Flows helps bring these important theorems to a broader mathematical readership.
Download or read book Control Theory and Optimization I written by M.I. Zelikin and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The only monograph on the topic, this book concerns geometric methods in the theory of differential equations with quadratic right-hand sides, closely related to the calculus of variations and optimal control theory. Based on the author’s lectures, the book is addressed to undergraduate and graduate students, and scientific researchers.
Download or read book Gradient Flows written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2008-10-29 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the theory of gradient flows in the general framework of metric spaces, and in the more specific setting of the space of probability measures, which provide a surprising link between optimal transportation theory and many evolutionary PDE's related to (non)linear diffusion. Particular emphasis is given to the convergence of the implicit time discretization method and to the error estimates for this discretization, extending the well established theory in Hilbert spaces. The book is split in two main parts that can be read independently of each other.
Download or read book Dynamics Geometry Number Theory written by David Fisher and published by University of Chicago Press. This book was released on 2022-02-07 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematicians David Fisher, Dmitry Kleinbock, and Gregory Soifer highlight in this edited collection the foundations and evolution of research by mathematician Gregory Margulis. Margulis is unusual in the degree to which his solutions to particular problems have opened new vistas of mathematics. Margulis' ideas were central, for example, to developments that led to the recent Fields Medals of Elon Lindenstrauss and Maryam Mirzhakhani. The broad goal of this volume is to introduce these areas, their development, their use in current research, and the connections between them. The foremost experts on the topic have written each of the chapters in this volume with a view to making them accessible by graduate students and by experts in other parts of mathematics"--
Download or read book On the Geometry of Diffusion Operators and Stochastic Flows written by K.D. Elworthy and published by Springer. This book was released on 2007-01-05 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, especially those with interests in stochastic flows, infinite dimensional analysis, or geometric analysis, and also to researchers in sub-Riemannian geometry. A basic background in differential geometry is assumed, but the construction of the connections is very direct and itself gives an intuitive and concrete introduction. Knowledge of stochastic analysis is also assumed for later chapters.
Download or read book Geometry Groups and Dynamics written by C. S. Aravinda and published by American Mathematical Soc.. This book was released on 2015-05-01 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Discrete Subgroups of Semisimple Lie Groups written by Gregori A. Margulis and published by Springer Science & Business Media. This book was released on 1991-02-15 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete subgroups have played a central role throughout the development of numerous mathematical disciplines. Discontinuous group actions and the study of fundamental regions are of utmost importance to modern geometry. Flows and dynamical systems on homogeneous spaces have found a wide range of applications, and of course number theory without discrete groups is unthinkable. This book, written by a master of the subject, is primarily devoted to discrete subgroups of finite covolume in semi-simple Lie groups. Since the notion of "Lie group" is sufficiently general, the author not only proves results in the classical geometry setting, but also obtains theorems of an algebraic nature, e.g. classification results on abstract homomorphisms of semi-simple algebraic groups over global fields. The treatise of course contains a presentation of the author's fundamental rigidity and arithmeticity theorems. The work in this monograph requires the language and basic results from fields such as algebraic groups, ergodic theory, the theory of unitary representatons, and the theory of amenable groups. The author develops the necessary material from these subjects; so that, while the book is of obvious importance for researchers working in related areas, it is essentially self-contained and therefore is also of great interest for advanced students.
Download or read book The Theory of Homogeneous Turbulence written by G. K. Batchelor and published by Cambridge University Press. This book was released on 1953 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reissue of Professor Batchelor's text on the theory of turbulent motion, which was first published by Cambridge Unviersity Press in 1953. It continues to be widely referred to in the professional literature of fluid mechanics, but has not been available for several years. This classic account includes an introduction to the study of homogeneous turbulence, including its mathematic representation and kinematics. Linear problems, such as the randomly-perturbed harmonic oscillator and turbulent flow through a wire gauze, are then treated. The author also presents the general dynamics of decay, universal equilibrium theory, and the decay of energy-containing eddies. There is a renewed interest in turbulent motion, which finds applications in atmospheric physics, fluid mechanics, astrophysics, and planetary science.
