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Author : Jürgen Moser
Publisher : American Mathematical Soc.
ISBN 13 : 0821812815
Total Pages : 92 pages
Book Rating : 4.8/5 (218 download)
Download or read book Lectures on Hamiltonian Systems written by Jürgen Moser and published by American Mathematical Soc.. This book was released on 1968 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Antonio Giorgilli
Publisher : Cambridge University Press
ISBN 13 : 100917486X
Total Pages : 474 pages
Book Rating : 4.0/5 (91 download)
Download or read book Notes on Hamiltonian Dynamical Systems Notes on Hamiltonian Dynamical Systems written by Antonio Giorgilli and published by Cambridge University Press. This book was released on 2022-05-05 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov–Arnold–Moser theorem, Nekhoroshev's theorem and superexponential stability. Its analytic approach allows students to learn about perturbation methods leading to advanced results. Key topics covered include Liouville's theorem, the proof of Poincaré's non-integrability theorem and the nonlinear dynamics in the neighbourhood of equilibria. The theorem of Kolmogorov on persistence of invariant tori and the theory of exponential stability of Nekhoroshev are proved via constructive algorithms based on the Lie series method. A final chapter is devoted to the discovery of chaos by Poincaré and its relations with integrability, also including recent results on superexponential stability. Written in an accessible, self-contained way with few prerequisites, this book can serve as an introductory text for senior undergraduate and graduate students.
Author : Walter Craig
Publisher : Springer Science & Business Media
ISBN 13 : 1402069642
Total Pages : 450 pages
Book Rating : 4.4/5 (2 download)
Download or read book Hamiltonian Dynamical Systems and Applications written by Walter Craig and published by Springer Science & Business Media. This book was released on 2008-02-17 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
Author : Jens Hoppe
Publisher : Springer Science & Business Media
ISBN 13 : 3540472746
Total Pages : 109 pages
Book Rating : 4.5/5 (44 download)
Download or read book Lectures on Integrable Systems written by Jens Hoppe and published by Springer Science & Business Media. This book was released on 2008-09-15 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mainly drawing on explicit examples, the author introduces the reader to themost recent techniques to study finite and infinite dynamical systems. Without any knowledge of differential geometry or lie groups theory the student can follow in a series of case studies the most recent developments. r-matrices for Calogero-Moser systems and Toda lattices are derived. Lax pairs for nontrivial infinite dimensionalsystems are constructed as limits of classical matrix algebras. The reader will find explanations of the approach to integrable field theories, to spectral transform methods and to solitons. New methods are proposed, thus helping students not only to understand established techniques but also to interest them in modern research on dynamical systems.
Author : CIME-EMS Summer School (
Publisher : Springer Science & Business Media
ISBN 13 : 9783540240648
Total Pages : 196 pages
Book Rating : 4.2/5 (46 download)
Download or read book Hamiltonian Dynamics Theory and Applications written by CIME-EMS Summer School ( and published by Springer Science & Business Media. This book was released on 2005 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A. Clebsch
Publisher : Springer
ISBN 13 : 9386279622
Total Pages : 351 pages
Book Rating : 4.3/5 (862 download)
Download or read book Jacobi's Lectures on Dynamics written by A. Clebsch and published by Springer. This book was released on 2009-08-15 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: The name of C. G. J. Jacobi is familiar to every student of mathematics, thanks to the Jacobion determinant, the Hamilton-Jacobi equations in dynamics, and the Jacobi identity for vector fields. Best known for his contributions to the theory of elliptic and abelian functions, Jacobi is also known for his innovative teaching methods and for running the first research seminar in pure mathematics. A record of his lectures on Dynamics given in 1842-43 at Konigsberg, edited by A. Clebsch, has been available in the original German. This is an English translation. It is not just a historical document; the modern reader can learn much about the subject directly from one of its great masters.
Author : Dmitry Treschev
Publisher : Springer Science & Business Media
ISBN 13 : 3642030289
Total Pages : 221 pages
Book Rating : 4.6/5 (42 download)
Download or read book Introduction to the Perturbation Theory of Hamiltonian Systems written by Dmitry Treschev and published by Springer Science & Business Media. This book was released on 2009-10-08 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an extended version of lectures given by the ?rst author in 1995–1996 at the Department of Mechanics and Mathematics of Moscow State University. We believe that a major part of the book can be regarded as an additional material to the standard course of Hamiltonian mechanics. In comparison with the original Russian 1 version we have included new material, simpli?ed some proofs and corrected m- prints. Hamiltonian equations ?rst appeared in connection with problems of geometric optics and celestial mechanics. Later it became clear that these equations describe a large classof systemsin classical mechanics,physics,chemistry,and otherdomains. Hamiltonian systems and their discrete analogs play a basic role in such problems as rigid body dynamics, geodesics on Riemann surfaces, quasi-classic approximation in quantum mechanics, cosmological models, dynamics of particles in an accel- ator, billiards and other systems with elastic re?ections, many in?nite-dimensional models in mathematical physics, etc. In this book we study Hamiltonian systems assuming that they depend on some parameter (usually?), where for?= 0 the dynamics is in a sense simple (as a rule, integrable). Frequently such a parameter appears naturally. For example, in celestial mechanics it is accepted to take? equal to the ratio: the mass of Jupiter over the mass of the Sun. In other cases it is possible to introduce the small parameter ar- ?cially.
Author : Jerrold E. Marsden
Publisher : Springer
ISBN 13 : 3540724702
Total Pages : 527 pages
Book Rating : 4.5/5 (47 download)
Download or read book Hamiltonian Reduction by Stages written by Jerrold E. Marsden and published by Springer. This book was released on 2007-06-05 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Jerrold E. Marsden
Publisher : Cambridge University Press
ISBN 13 : 9780521428446
Total Pages : 272 pages
Book Rating : 4.4/5 (284 download)
Download or read book Lectures on Mechanics written by Jerrold E. Marsden and published by Cambridge University Press. This book was released on 1992-04-30 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the 1991 LMS Invited Lectures given by Professor Marsden, this book discusses and applies symmetry methods to such areas as bifurcations and chaos in mechanical systems.
Author : Jürgen Moser
Publisher : American Mathematical Soc.
ISBN 13 : 0821835777
Total Pages : 266 pages
Book Rating : 4.8/5 (218 download)
Download or read book Notes on Dynamical Systems written by Jürgen Moser and published by American Mathematical Soc.. This book was released on 2005 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the field of dynamical systems, in particular, to the special class of Hamiltonian systems. The authors aimed at keeping the requirements of mathematical techniques minimal but giving detailed proofs and many examples and illustrations from physics and celestial mechanics. After all, the celestial $N$-body problem is the origin of dynamical systems and gave rise in the past to many mathematical developments. Jurgen Moser (1928-1999) was a professor atthe Courant Institute, New York, and then at ETH Zurich. He served as president of the International Mathematical Union and received many honors and prizes, among them the Wolf Prize in mathematics. Jurgen Moser is the author of several books, among them Stable and Random Motions in DynamicalSystems. Eduard Zehnder is a professor at ETH Zurich. He is coauthor with Helmut Hofer of the book Symplectic Invariants and Hamiltonian Dynamics. Information for our distributors: Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
Author : Ana Cannas da Silva
Publisher : Springer
ISBN 13 : 354045330X
Total Pages : 240 pages
Book Rating : 4.5/5 (44 download)
Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Author : Jurgen Moser
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (875 download)
Download or read book Lectures on Hamiltonian Systems written by Jurgen Moser and published by . This book was released on 1968 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Helmut Hofer
Publisher : Birkhäuser
ISBN 13 : 3034885407
Total Pages : 356 pages
Book Rating : 4.0/5 (348 download)
Download or read book Symplectic Invariants and Hamiltonian Dynamics written by Helmut Hofer and published by Birkhäuser. This book was released on 2012-12-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis of an old variational principal in classical mechanics has established global periodic phenomena in Hamiltonian systems. One of the links is a class of sympletic invariants, called sympletic capacities, and these invariants are the main theme of this book. Topics covered include basic sympletic geometry, sympletic capacities and rigidity, sympletic fixed point theory, and a survey on Floer homology and sympletic homology.
Author : Patrick Hamill
Publisher : Cambridge University Press
ISBN 13 : 1107042887
Total Pages : 185 pages
Book Rating : 4.1/5 (7 download)
Download or read book A Student's Guide to Lagrangians and Hamiltonians written by Patrick Hamill and published by Cambridge University Press. This book was released on 2014 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise treatment of variational techniques, focussing on Lagrangian and Hamiltonian systems, ideal for physics, engineering and mathematics students.
Author : Paul A. M. Dirac
Publisher : Courier Corporation
ISBN 13 : 0486320286
Total Pages : 100 pages
Book Rating : 4.4/5 (863 download)
Download or read book Lectures on Quantum Mechanics written by Paul A. M. Dirac and published by Courier Corporation. This book was released on 2013-05-27 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Four concise, brilliant lectures on mathematical methods in quantum mechanics from Nobel Prize–winning quantum pioneer build on idea of visualizing quantum theory through the use of classical mechanics.
Author : Jürgen Moser
Publisher : Edizioni della Normale
ISBN 13 : 9788876422522
Total Pages : 0 pages
Book Rating : 4.4/5 (225 download)
Download or read book Integrable Hamiltonian systems and spectral theory written by Jürgen Moser and published by Edizioni della Normale. This book was released on 1983-10-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on six Fermi Lectures held at the Scuola Normale Superiore in Pisa in March and April 1981. The topics treated depend on basic concepts of classical mechanics, elementary geometry, complex analysis as well as spectral theory and are meant for mathematicians and theoretical physicists alike. These lectures weave together a number of threads from various fields of mathematics impinging on the subject of inverse spectral theory. I did not try to give an overview over this fast moving subject but rather tie various aspects together by one guiding theme: the construction of all potentials for the one-dimensional Schrödinger equation which gives rise to finite band potentials, which is done by reducing it to solving a system of differential equations. In fact, we will see that the problem of finding all almost periodic potentials having finitely many intervals as its spectrum is equivalent to the study of the geodesics on an ellipsoid. To make this connection clear we have carried together several facts from classical mechanics and from spectral theory and we give a self-contained exposition of the construction of these finite band potentials.
Author : R.S MacKay
Publisher : CRC Press
ISBN 13 : 9780852742051
Total Pages : 808 pages
Book Rating : 4.7/5 (42 download)
Download or read book Hamiltonian Dynamical Systems written by R.S MacKay and published by CRC Press. This book was released on 1987-01-01 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics.
