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Dynamics On Lorentz Manifolds
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Book Synopsis Dynamics On Lorentz Manifolds by : Scot Adams
Download or read book Dynamics On Lorentz Manifolds written by Scot Adams and published by World Scientific. This book was released on 2001-11-19 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the general framework of the dynamics of “large” groups on geometric spaces, the focus is on the types of groups that can act in complicated ways on Lorentz manifolds, and on the structure of the resulting manifolds and actions. This particular area of dynamics is an active one, and not all the results are in their final form. However, at this point, a great deal can be said about the particular Lie groups that come up in this context. It is impressive that, even assuming very weak recurrence of the action, the list of possible groups is quite restricted. For the most complicated of these groups, one can also describe reasonably well the local structure of the actions that arise.This advanced text is also appropriate to a course for mathematics graduate students who have completed their first year of study.
Book Synopsis Dynamics on Lorentz Manifolds by : Scot Adams
Download or read book Dynamics on Lorentz Manifolds written by Scot Adams and published by World Scientific. This book was released on 2001 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the general framework of the dynamics of OC largeOCO groups on geometric spaces, the focus is on the types of groups that can act in complicated ways on Lorentz manifolds, and on the structure of the resulting manifolds and actions. This particular area of dynamics is an active one, and not all the results are in their final form. However, at this point, a great deal can be said about the particular Lie groups that come up in this context. It is impressive that, even assuming very weak recurrence of the action, the list of possible groups is quite restricted. For the most complicated of these groups, one can also describe reasonably well the local structure of the actions that arise. This advanced text is also appropriate to a course for mathematics graduate students who have completed their first year of study. Contents: Introduction, History and Outline; Basic Results and Definitions; Basic Differential Topology; Basic Lie Theoretic Results; More Lie Theory; Minkowski Linear Algebra; Basic Dynamical Results; Examples of Actions on Compact Lorentz Manifolds; Examples of Nonproper Actions; Semisimple Groups Admitting a Nonproper Action; Groups with Action on a Compact Lorentz Manifold; The Isometry Group of a Compact Lorentz Manifold; Highly Symmetric Compact Lorentz Manifolds; Locally Free Orbit Nonproper Lorentz Actions; Orbit Nonproper Lorentz Actions; Appendices: The Borel Density Theorem; Tameness of Algebraic Actions in Characteristic Zero. Readership: Researchers and graduate students in mathematics, mathematical physics and theoretical physics."
Book Synopsis Classical Particle Dynamics on Homogeneous Lorentz Manifolds by : Stephan DeBièvre
Download or read book Classical Particle Dynamics on Homogeneous Lorentz Manifolds written by Stephan DeBièvre and published by . This book was released on 1984 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Manifolds and Theoretical Physics by :
Download or read book Differential Manifolds and Theoretical Physics written by and published by Academic Press. This book was released on 1985-05-24 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Manifolds and Theoretical Physics
Author :Dmitriĭ Vladimirovich Alekseevskiĭ Publisher :European Mathematical Society ISBN 13 :9783037190517 Total Pages :556 pages Book Rating :4.1/5 (95 download)
Book Synopsis Recent Developments in Pseudo-Riemannian Geometry by : Dmitriĭ Vladimirovich Alekseevskiĭ
Download or read book Recent Developments in Pseudo-Riemannian Geometry written by Dmitriĭ Vladimirovich Alekseevskiĭ and published by European Mathematical Society. This book was released on 2008 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are: Classification of pseudo-Riemannian symmetric spaces Holonomy groups of Lorentzian and pseudo-Riemannian manifolds Hypersymplectic manifolds Anti-self-dual conformal structures in neutral signature and integrable systems Neutral Kahler surfaces and geometric optics Geometry and dynamics of the Einstein universe Essential conformal structures and conformal transformations in pseudo-Riemannian geometry The causal hierarchy of spacetimes Geodesics in pseudo-Riemannian manifolds Lorentzian symmetric spaces in supergravity Generalized geometries in supergravity Einstein metrics with Killing leaves The book is addressed to advanced students as well as to researchers in differential geometry, global analysis, general relativity and string theory. It shows essential differences between the geometry on manifolds with positive definite metrics and on those with indefinite metrics, and highlights the interesting new geometric phenomena, which naturally arise in the indefinite metric case. The reader finds a description of the present state of the art in the field as well as open problems, which can stimulate further research.
Book Synopsis Flat Lorentz 3-Manifolds by : Louis Auslander
Download or read book Flat Lorentz 3-Manifolds written by Louis Auslander and published by American Mathematical Soc.. This book was released on 1959 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Manifold Theory written by D. Martin and published by Horwood Publishing. This book was released on 2002-03-15 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive account of basic manifold theory for post graduate students. Contains more than 130 exercises, with helpful hints and solutions and introduces the basic theory of differential geometry to students in theoretical physics and mathematics.
Book Synopsis Compact Lorentz Manifolds with Local Symmetry by : Karin Melnick
Download or read book Compact Lorentz Manifolds with Local Symmetry written by Karin Melnick and published by . This book was released on 2006 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric Dynamics by : Constantin Udriște
Download or read book Geometric Dynamics written by Constantin Udriște and published by Springer Science & Business Media. This book was released on 2000 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theme of this text is the philosophy that any particle flow generates a particle dynamics, in a suitable geometrical framework. It covers topics that include: geometrical and physical vector fields; field lines; flows; stability of equilibrium points; potential systems and catastrophe geometry; field hypersurfaces; bifurcations; distribution orthogonal to a vector field; extrema with nonholonomic constraints; thermodynamic systems; energies; geometric dynamics induced by a vector field; magnetic fields around piecewise rectilinear electric circuits; geometric magnetic dynamics; and granular materials and their mechanical behaviour. The text should be useful for first-year graduate students in mathematics, mechanics, physics, engineering, biology, chemistry, and economics. It can also be addressed to professors and researchers whose work involves mathematics, mechanics, physics, engineering, biology, chemistry, and economics.
Book Synopsis Group Representations, Ergodic Theory, and Mathematical Physics by : Robert S. Doran
Download or read book Group Representations, Ergodic Theory, and Mathematical Physics written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 2008 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics.
Download or read book Mechanics written by Florian Scheck and published by Springer Science & Business Media. This book was released on 2010-04-01 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Purpose and Emphasis. Mechanics not only is the oldest branch of physics but was and still is the basis for all of theoretical physics. Quantum mechanics can hardly be understood, perhaps cannot even be formulated, without a good kno- edge of general mechanics. Field theories such as electrodynamics borrow their formal framework and many of their building principles from mechanics. In short, throughout the many modern developments of physics where one frequently turns back to the principles of classical mechanics its model character is felt. For this reason it is not surprising that the presentation of mechanics re?ects to some - tent the development of modern physics and that today this classical branch of theoretical physics is taught rather differently than at the time of Arnold S- merfeld, in the 1920s, or even in the 1950s, when more emphasis was put on the theoryandtheapplicationsofpartial-differentialequations. Today, symmetriesand invariance principles, the structure of the space–time continuum, and the geom- rical structure of mechanics play an important role. The beginner should realize that mechanics is not primarily the art of describing block-and-tackles, collisions of billiard balls, constrained motions of the cylinder in a washing machine, or - cycle riding.
Download or read book Mechanics written by Florian A. Scheck and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: A course in mechanics is of primary importance in any physics teaching program. Scheck's book integrates the various aspects of classical mechanics, relativistic mechanics, and modern topics such as deterministic chaos. Both the physical approach to mechanics and its mathematical foundations are emphasised. With elementary Newtonian mechanics as a starting point, the principles of canonical mechanics in Hamiltonian and Lagrangian formulations are outlined. Rigid bodies are treated in detail, and the basic concepts of special relativity are given. Particular emphasis is put on the geometrical aspects of mechanics, such as geometrical objects on manifolds. A chapter on stability and chaos concludes the book, introducing topics such as the long-time behavior of dynamical flows, deterministic chaos, and chaotic motion in celestial mechanics.
Book Synopsis Geometry, Mechanics, and Dynamics by : Paul Newton
Download or read book Geometry, Mechanics, and Dynamics written by Paul Newton and published by Springer Science & Business Media. This book was released on 2006-05-11 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jerry Marsden, one of the world’s pre-eminent mechanicians and applied mathematicians, celebrated his 60th birthday in August 2002. The event was marked by a workshop on “Geometry, Mechanics, and Dynamics”at the Fields Institute for Research in the Mathematical Sciences, of which he wasthefoundingDirector. Ratherthanmerelyproduceaconventionalp- ceedings, with relatively brief accounts of research and technical advances presented at the meeting, we wished to acknowledge Jerry’s in?uence as a teacher, a propagator of new ideas, and a mentor of young talent. Con- quently, starting in 1999, we sought to collect articles that might be used as entry points by students interested in ?elds that have been shaped by Jerry’s work. At the same time we hoped to give experts engrossed in their own technical niches an indication of the wonderful breadth and depth of their subjects as a whole. This book is an outcome of the e?orts of those who accepted our in- tations to contribute. It presents both survey and research articles in the several ?elds that represent the main themes of Jerry’s work, including elasticity and analysis, ?uid mechanics, dynamical systems theory, g- metric mechanics, geometric control theory, and relativity and quantum mechanics. The common thread running through this broad tapestry is the use of geometric methods that serve to unify diverse disciplines and bring a widevarietyofscientistsandmathematicianstogether,speakingalanguage which enhances dialogue and encourages cross-fertilization.
Book Synopsis Invariant Manifolds and Dispersive Hamiltonian Evolution Equations by : Kenji Nakanishi
Download or read book Invariant Manifolds and Dispersive Hamiltonian Evolution Equations written by Kenji Nakanishi and published by European Mathematical Society. This book was released on 2011 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of an invariant manifold arises naturally in the asymptotic stability analysis of stationary or standing wave solutions of unstable dispersive Hamiltonian evolution equations such as the focusing semilinear Klein-Gordon and Schrodinger equations. This is due to the fact that the linearized operators about such special solutions typically exhibit negative eigenvalues (a single one for the ground state), which lead to exponential instability of the linearized flow and allows for ideas from hyperbolic dynamics to enter. One of the main results proved here for energy subcritical equations is that the center-stable manifold associated with the ground state appears as a hyper-surface which separates a region of finite-time blowup in forward time from one which exhibits global existence and scattering to zero in forward time. The authors' entire analysis takes place in the energy topology, and the conserved energy can exceed the ground state energy only by a small amount. This monograph is based on recent research by the authors. The proofs rely on an interplay between the variational structure of the ground states and the nonlinear hyperbolic dynamics near these states. A key element in the proof is a virial-type argument excluding almost homoclinic orbits originating near the ground states, and returning to them, possibly after a long excursion. These lectures are suitable for graduate students and researchers in partial differential equations and mathematical physics. For the cubic Klein-Gordon equation in three dimensions all details are provided, including the derivation of Strichartz estimates for the free equation and the concentration-compactness argument leading to scattering due to Kenig and Merle.
Book Synopsis Geometry, Topology and Dynamics of Character Varieties by : William Mark Goldman
Download or read book Geometry, Topology and Dynamics of Character Varieties written by William Mark Goldman and published by World Scientific. This book was released on 2012 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to describe, for readers uneducated in science, the development of humanity's desire to know and understand the world around us through the various stages of its development to the present, when science is almost universally recognized - at least in the Western world - as the most reliable way of knowing. The book describes the history of the large-scale exploration of the surface of the earth by sea, beginning with the Vikings and the Chinese, and of the unknown interiors of the American and African continents by foot and horseback. After the invention of the telescope, visual exploration of the surfaces of the Moon and Mars were made possible, and finally a visit to the Moon. The book then turns to our legacy from the ancient Greeks of wanting to understand rather than just know, and why the scientific way of understanding is valued. For concreteness, it relates the lives and accomplishments of six great scientists, four from the nineteenth century and two from the twentieth. Finally, the book explains how chemistry came to be seen as the most basic of the sciences, and then how physics became the most fundamental.
Book Synopsis The Einstein Equations and the Large Scale Behavior of Gravitational Fields by : Piotr T. Chrusciel
Download or read book The Einstein Equations and the Large Scale Behavior of Gravitational Fields written by Piotr T. Chrusciel and published by Birkhäuser. This book was released on 2012-12-06 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions. It combines in a unique way introductory chapters and surveys of various aspects of the analysis of the Einstein equations in the large. It discusses applications of the Einstein equations in geometrical studies and the physical interpretation of their solutions. Open problems concerning analytical and numerical aspects of the Einstein equations are pointed out. Background material on techniques in PDE theory, differential geometry, and causal theory is provided.
Book Synopsis Time and Timelessness in Fundamental Physics and Cosmology by : Silvia De Bianchi
Download or read book Time and Timelessness in Fundamental Physics and Cosmology written by Silvia De Bianchi and published by Springer Nature. This book was released on with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt:
