A Geometric Setting For Hamiltonian Perturbation Theory
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A Geometric Setting For Hamiltonian Perturbation Theory
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Author : Anthony D. Blaom
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
A Geometric Setting For Hamiltonian Perturbation Theory written by Anthony D. Blaom 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.
In this text, the perturbation theory of non-commutatively integrable systems is revisited from the point of view of non-Abelian symmetry groups. Using a co-ordinate system intrinsic to the geometry of the symmetry, the book generalizes and geometrizes well-known estimates of Nekhoroshev (1977), in a class of systems having almost $G$-invariant Hamiltonians. These estimates are shown to have a natural interpretation in terms of momentum maps and co-adjoint orbits. The geometric framework adopted is described explicitly in examples, including the Euler-Poinsot rigid body.
A Geometric Setting For Hamiltonian Perturbation Theory
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Author : Anthony D. Blaom
language : en
Publisher:
Release Date : 2014-09-11
A Geometric Setting For Hamiltonian Perturbation Theory written by Anthony D. Blaom and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Hamiltonian systems categories.
Introduction Part 1. Dynamics: Lie-Theoretic preliminaries Action-group coordinates On the existence of action-group coordinates Naive averaging An abstract formulation of Nekhoroshev's theorem Applying the abstract Nekhoroshev's theorem to action-group coordinates Nekhoroshev-type estimates for momentum maps Part 2. Geometry: On Hamiltonian $G$-spaces with regular momenta Action-group coordinates as a symplectic cross-section Constructing action-group coordinates The axisymmetric Euler-Poinsot rigid body Passing from dynamic integrability to geometric integrability Concluding remarks Appendix A. Proof of the Nekhoroshev-Lochak theorem Appendix B. Proof the ${\mathcal W}$ is a slice Appendix C. Proof of the extension lemma Appendix D. An application of converting dynamic integrability into geometric integrability: The Euler-Poinsot rigid body revisited Appendix E. Dual pairs, leaf correspondence, and symplectic reduction Bibliography.
Perturbation Theory
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Author : Giuseppe Gaeta
language : en
Publisher: Springer Nature
Release Date : 2022-12-16
Perturbation Theory written by Giuseppe Gaeta and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-16 with Science categories.
This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.
The Ab Program In Geometric Analysis Sharp Sobolev Inequalities And Related Problems
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Author : Olivier Druet
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
The Ab Program In Geometric Analysis Sharp Sobolev Inequalities And Related Problems written by Olivier Druet 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 2002 with Mathematics categories.
Function theory and Sobolev inequalities have been the target of investigation for many years. Sharp constants in these inequalities constitute a critical tool in geometric analysis. The $AB$ programme is concerned with sharp Sobolev inequalities on compact Riemannian manifolds. This text summarizes the results of contemporary research and gives an up-to-date report on the field.
Quantum Algebras And Poisson Geometry In Mathematical Physics
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Author : Mikhail Vladimirovich Karasev
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Quantum Algebras And Poisson Geometry In Mathematical Physics written by Mikhail Vladimirovich Karasev 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 2005 with Computers categories.
This collection presents new and interesting applications of Poisson geometry to some fundamental well-known problems in mathematical physics. In addition to advanced Poisson geometry, the methods used by the authors include unexpected algebras with non-Lie commutation relations, nontrivial (quantum) Kahlerian structures of hypergeometric type, dynamical systems theory, semiclassical asymptotics, and more. The volume is suitable for graduate students and researchers interested in mathematical physics. Other AMS publications by M. Karasev include ""Nonlinear Poisson Brackets""; ""Geometry and Quantization"", ""Coherent Transform, Quantization, and Poisson Geometry"", and ""Asymptotic Methods for Wave and Quantum Problems"".
The Breadth Of Symplectic And Poisson Geometry
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Author : Jerrold E. Marsden
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-03
The Breadth Of Symplectic And Poisson Geometry written by Jerrold E. Marsden 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 2007-07-03 with Mathematics categories.
* The invited papers in this volume are written in honor of Alan Weinstein, one of the world’s foremost geometers * Contributions cover a broad range of topics in symplectic and differential geometry, Lie theory, mechanics, and related fields * Intended for graduate students and working mathematicians, this text is a distillation of prominent research and an indication of future trends in geometry, mechanics, and mathematical physics
Homotopy Theory Of The Suspensions Of The Projective Plane
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Author : Jie Wu
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Homotopy Theory Of The Suspensions Of The Projective Plane written by Jie Wu 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 2003 with Mathematics categories.
Investigates the homotopy theory of the suspensions of the real projective plane. This book computes the homotopy groups up to certain range. It also studies the decompositions of the self smashes and the loop spaces with some applications to the Stiefel manifolds.
The Submanifold Geometries Associated To Grassmannian Systems
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Author : Martina Brück
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
The Submanifold Geometries Associated To Grassmannian Systems written by Martina Brück 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 2002 with Mathematics categories.
This work is intended for graduate students and research mathematicians interested in differential geometry and partial differential equations.
From Representation Theory To Homotopy Groups
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Author : Donald M. Davis
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
From Representation Theory To Homotopy Groups written by Donald M. Davis 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 2002 with Mathematics categories.
A formula for the odd-primary v1-periodic homotopy groups of a finite H-space in terms of its K-theory and Adams operations has been obtained by Bousfield. This work applys this theorem to give explicit determinations of the v1-periodic homotopy groups of (E8,5) and (E8,3), thus completing the determination of all odd-primary v1-periodic homotopy groups of all compact simple Lie groups, a project suggested by Mimura in 1989.
Homotopy Theory Of Diagrams
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Author : Wojciech Chachólski
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Homotopy Theory Of Diagrams written by Wojciech Chachólski 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 2002 with Mathematics categories.
In this paper the authors develop homotopy theoretical methods for studying diagrams. In particular they explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept introduced is that of a model approximation. A model approximation of a category $\mathcal{C}$ with a given class of weak equivalences is a model category $\mathcal{M}$ together with a pair of adjoint functors $\mathcal{M} \rightleftarrows \mathcal{C}$ which satisfy certain properties. The key result says that if $\mathcal{C}$ admits a model approximation then so does the functor category $Fun(I, \mathcal{C})$.