The Principle Of Least Action In Geometry And Dynamics
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The Principle Of Least Action In Geometry And Dynamics
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Author : Karl Friedrich Siburg
language : en
Publisher: Springer
Release Date : 2004-04-30
The Principle Of Least Action In Geometry And Dynamics written by Karl Friedrich Siburg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-30 with Mathematics categories.
New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards, length spectrum, Hofer geometry, modern symplectic geometry). Thus, topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mather’s minimal action functional. The level is for graduate students onwards, but also for researchers in any of the subjects touched in the book.
The Principle Of Least Action In Geometry And Dynamics
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Author : Karl Friedrich Siburg
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-05-17
The Principle Of Least Action In Geometry And Dynamics written by Karl Friedrich Siburg 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 2004-05-17 with Computers categories.
New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards, length spectrum, Hofer geometry, modern symplectic geometry). Thus, topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mather’s minimal action functional. The level is for graduate students onwards, but also for researchers in any of the subjects touched in the book.
The Principle Of Least Action
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Author : Alberto G. Rojo
language : en
Publisher: Cambridge University Press
Release Date : 2018-03-29
The Principle Of Least Action written by Alberto G. Rojo 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 2018-03-29 with Mathematics categories.
This text brings history and the key fields of physics together to present a unique technical discussion of the principles of least action.
The Ricci Flow In Riemannian Geometry
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Author : Ben Andrews
language : en
Publisher: Springer Science & Business Media
Release Date : 2011
The Ricci Flow In Riemannian Geometry written by Ben Andrews 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 2011 with Mathematics categories.
This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.
Geometric Properties Of Banach Spaces And Nonlinear Iterations
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Author : Charles Chidume
language : en
Publisher: Springer
Release Date : 2008-12-21
Geometric Properties Of Banach Spaces And Nonlinear Iterations written by Charles Chidume and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-21 with Mathematics categories.
The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.
Random Perturbation Of Pdes And Fluid Dynamic Models
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Author : Franco Flandoli
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-11
Random Perturbation Of Pdes And Fluid Dynamic Models written by Franco Flandoli 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 2011-03-11 with Mathematics categories.
This volume explores the random perturbation of PDEs and fluid dynamic models. The text describes the role of additive and bilinear multiplicative noise, and includes examples of abstract parabolic evolution equations.
Foundations Of Grothendieck Duality For Diagrams Of Schemes
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Author : Joseph Lipman
language : en
Publisher: Springer
Release Date : 2009-03-07
Foundations Of Grothendieck Duality For Diagrams Of Schemes written by Joseph Lipman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-07 with Mathematics categories.
Part One of this book covers the abstract foundations of Grothendieck duality theory for schemes in part with noetherian hypotheses and with some refinements for maps of finite tor-dimension. Part Two extends the theory to the context of diagrams of schemes.
Topics In Algebraic And Topological K Theory
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Author : Paul Frank Baum
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-05
Topics In Algebraic And Topological K Theory written by Paul Frank Baum 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 2010-11-05 with Mathematics categories.
This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.
Hamiltonian Reduction By Stages
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Author : Jerrold E. Marsden
language : en
Publisher: Springer
Release Date : 2007-06-05
Hamiltonian Reduction By Stages written by Jerrold E. Marsden and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-05 with Mathematics categories.
This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.
Feynman S Thesis
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Author : Richard Phillips Feynman
language : en
Publisher: World Scientific
Release Date : 2005
Feynman S Thesis written by Richard Phillips Feynman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
Richard Feynman's never previously published doctoral thesis formed the heart of much of his brilliant and profound work in theoretical physics. Entitled ?The Principle of Least Action in Quantum Mechanics," its original motive was to quantize the classical action-at-a-distance electrodynamics. Because that theory adopted an overall space?time viewpoint, the classical Hamiltonian approach used in the conventional formulations of quantum theory could not be used, so Feynman turned to the Lagrangian function and the principle of least action as his points of departure.The result was the path integral approach, which satisfied ? and transcended ? its original motivation, and has enjoyed great success in renormalized quantum field theory, including the derivation of the ubiquitous Feynman diagrams for elementary particles. Path integrals have many other applications, including atomic, molecular, and nuclear scattering, statistical mechanics, quantum liquids and solids, Brownian motion, and noise theory. It also sheds new light on fundamental issues like the interpretation of quantum theory because of its new overall space?time viewpoint.The present volume includes Feynman's Princeton thesis, the related review article ?Space?Time Approach to Non-Relativistic Quantum Mechanics? [Reviews of Modern Physics 20 (1948), 367?387], Paul Dirac's seminal paper ?The Lagrangian in Quantum Mechanics'' [Physikalische Zeitschrift der Sowjetunion, Band 3, Heft 1 (1933)], and an introduction by Laurie M Brown.