Lectures on Hamiltonian Systems
Author: Jürgen Moser
Publisher: American Mathematical Soc.
Published: 1968
Total Pages: 92
ISBN-13: 0821812815
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Notes on Hamiltonian Dynamical Systems Notes on Hamiltonian Dynamical Systems
Author: Antonio Giorgilli
Publisher: Cambridge University Press
Published: 2022-05-05
Total Pages: 474
ISBN-13: 100917486X
DOWNLOAD EBOOKStarting 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.
Hamiltonian Dynamical Systems and Applications
Author: Walter Craig
Publisher: Springer Science & Business Media
Published: 2008-02-17
Total Pages: 450
ISBN-13: 1402069642
DOWNLOAD EBOOKThis 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.
Lectures on Integrable Systems
Author: Jens Hoppe
Publisher: Springer Science & Business Media
Published: 2008-09-15
Total Pages: 109
ISBN-13: 3540472746
DOWNLOAD EBOOKMainly 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.
Introduction to the Perturbation Theory of Hamiltonian Systems
Author: Dmitry Treschev
Publisher: Springer Science & Business Media
Published: 2009-10-08
Total Pages: 221
ISBN-13: 3642030289
DOWNLOAD EBOOKThis 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.
Jacobi's Lectures on Dynamics
Author: A. Clebsch
Publisher: Springer
Published: 2009-08-15
Total Pages: 351
ISBN-13: 9386279622
DOWNLOAD EBOOKThe 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.
Hamiltonian Dynamics Theory and Applications
Author: CIME-EMS Summer School (
Publisher: Springer Science & Business Media
Published: 2005
Total Pages: 196
ISBN-13: 9783540240648
DOWNLOAD EBOOKHamiltonian Reduction by Stages
Author: Jerrold E. Marsden
Publisher: Springer
Published: 2007-06-05
Total Pages: 527
ISBN-13: 3540724702
DOWNLOAD EBOOKThis 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.
Lectures on Mechanics
Author: Jerrold E. Marsden
Publisher: Cambridge University Press
Published: 1992-04-30
Total Pages: 272
ISBN-13: 9780521428446
DOWNLOAD EBOOKBased 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.
Lectures on Symplectic Geometry
Author: Ana Cannas da Silva
Publisher: Springer
Published: 2004-10-27
Total Pages: 240
ISBN-13: 354045330X
DOWNLOAD EBOOKThe 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.
