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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 : 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 : Eduard Zehnder
Publisher : European Mathematical Society
ISBN 13 : 9783037190814
Total Pages : 372 pages
Book Rating : 4.1/5 (98 download)
Download or read book Lectures on Dynamical Systems written by Eduard Zehnder and published by European Mathematical Society. This book was released on 2010 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book originated from an introductory lecture course on dynamical systems given by the author for advanced students in mathematics and physics at ETH Zurich. The first part centers around unstable and chaotic phenomena caused by the occurrence of homoclinic points. The existence of homoclinic points complicates the orbit structure considerably and gives rise to invariant hyperbolic sets nearby. The orbit structure in such sets is analyzed by means of the shadowing lemma, whose proof is based on the contraction principle. This lemma is also used to prove S. Smale's theorem about the embedding of Bernoulli systems near homoclinic orbits. The chaotic behavior is illustrated in the simple mechanical model of a periodically perturbed mathematical pendulum. The second part of the book is devoted to Hamiltonian systems. The Hamiltonian formalism is developed in the elegant language of the exterior calculus. The theorem of V. Arnold and R. Jost shows that the solutions of Hamiltonian systems which possess sufficiently many integrals of motion can be written down explicitly and for all times. The existence proofs of global periodic orbits of Hamiltonian systems on symplectic manifolds are based on a variational principle for the old action functional of classical mechanics. The necessary tools from variational calculus are developed. There is an intimate relation between the periodic orbits of Hamiltonian systems and a class of symplectic invariants called symplectic capacities. From these symplectic invariants one derives surprising symplectic rigidity phenomena. This allows a first glimpse of the fast developing new field of symplectic topology.
Author : Ernesto A Lacomba
Publisher : World Scientific
ISBN 13 : 9814553166
Total Pages : 218 pages
Book Rating : 4.8/5 (145 download)
Download or read book Hamiltonian Systems And Celestial Mechanics written by Ernesto A Lacomba and published by World Scientific. This book was released on 1993-04-30 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume puts together several important lectures on the Hamiltonian Systems and Celestial Mechanics to form a comprehensive and authoritative collection of works on the subject. The papers presented in this volume are an outgrowth of the lectures that took place during the 'International Symposium on Hamiltonian Systems and Celestial Mechanics', which was held at the CIMAT (Centro de Investigacion en Matematicas, Guanajuato, Mexico) from September 30 to October 4, 1991. In general, the lectures explored the subject of the Hamiltonian Dynamics and Celestial Mechanics and emphasized its relationship with several aspects of topology, mechanics and dynamical systems.
Author : Jürgen Moser
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (422 download)
Download or read book Lectures on Hamiltonian Systems written by Jürgen Moser and published by . This book was released on 1968 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : 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 : Giancarlo Benettin
Publisher : Springer
ISBN 13 : 3540315411
Total Pages : 187 pages
Book Rating : 4.5/5 (43 download)
Download or read book Hamiltonian Dynamics - Theory and Applications written by Giancarlo Benettin and published by Springer. This book was released on 2005-01-14 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume compiles three series of lectures on applications of the theory of Hamiltonian systems, contributed by some of the specialists in the field. The aim is to describe the state of the art for some interesting problems, such as the Hamiltonian theory for infinite-dimensional Hamiltonian systems, including KAM theory, the recent extensions of the theory of adiabatic invariants, and the phenomena related to stability over exponentially long times of Nekhoroshev's theory. The books may serve as an excellent basis for young researchers, who will find here a complete and accurate exposition of recent original results and many hints for further investigation.
Author : R. Clark Robinson
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (819 download)
Download or read book Lectures on hamiltonian systems written by R. Clark Robinson and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robinson Clark
Publisher :
ISBN 13 :
Total Pages : 83 pages
Book Rating : 4.:/5 (848 download)
Download or read book Lectures on Hamiltonian Systems written by Robinson Clark and published by . This book was released on 1971 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kenneth R. Meyer
Publisher : Springer
ISBN 13 : 3319536915
Total Pages : 389 pages
Book Rating : 4.3/5 (195 download)
Download or read book Introduction to Hamiltonian Dynamical Systems and the N-Body Problem written by Kenneth R. Meyer and published by Springer. This book was released on 2017-05-04 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition text provides expanded material on the restricted three body problem and celestial mechanics. With each chapter containing new content, readers are provided with new material on reduction, orbifolds, and the regularization of the Kepler problem, all of which are provided with applications. The previous editions grew out of graduate level courses in mathematics, engineering, and physics given at several different universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. This text provides a mathematical structure of celestial mechanics ideal for beginners, and will be useful to graduate students and researchers alike. Reviews of the second edition: "The primary subject here is the basic theory of Hamiltonian differential equations studied from the perspective of differential dynamical systems. The N-body problem is used as the primary example of a Hamiltonian system, a touchstone for the theory as the authors develop it. This book is intended to support a first course at the graduate level for mathematics and engineering students. ... It is a well-organized and accessible introduction to the subject ... . This is an attractive book ... ." (William J. Satzer, The Mathematical Association of America, March, 2009) “The second edition of this text infuses new mathematical substance and relevance into an already modern classic ... and is sure to excite future generations of readers. ... This outstanding book can be used not only as an introductory course at the graduate level in mathematics, but also as course material for engineering graduate students. ... it is an elegant and invaluable reference for mathematicians and scientists with an interest in classical and celestial mechanics, astrodynamics, physics, biology, and related fields.” (Marian Gidea, Mathematical Reviews, Issue 2010 d)
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 : Rex Clark Robinson
Publisher :
ISBN 13 :
Total Pages : 83 pages
Book Rating : 4.:/5 (783 download)
Download or read book Lectures on Hamiltonian Systems written by Rex Clark Robinson and published by . This book was released on 1971 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tudor Ratiu
Publisher : Springer Science & Business Media
ISBN 13 : 1461397251
Total Pages : 526 pages
Book Rating : 4.4/5 (613 download)
Download or read book The Geometry of Hamiltonian Systems written by Tudor Ratiu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume are an outgrowth of the lectures and informal discussions that took place during the workshop on "The Geometry of Hamiltonian Systems" which was held at MSRl from June 5 to 16, 1989. It was, in some sense, the last major event of the year-long program on Symplectic Geometry and Mechanics. The emphasis of all the talks was on Hamiltonian dynamics and its relationship to several aspects of symplectic geometry and topology, mechanics, and dynamical systems in general. The organizers of the conference were R. Devaney (co-chairman), H. Flaschka (co-chairman), K. Meyer, and T. Ratiu. The entire meeting was built around two mini-courses of five lectures each and a series of two expository lectures. The first of the mini-courses was given by A. T. Fomenko, who presented the work of his group at Moscow University on the classification of integrable systems. The second mini course was given by J. Marsden of UC Berkeley, who spoke about several applications of symplectic and Poisson reduction to problems in stability, normal forms, and symmetric Hamiltonian bifurcation theory. Finally, the two expository talks were given by A. Fathi of the University of Florida who concentrated on the links between symplectic geometry, dynamical systems, and Teichmiiller theory.
Author : Jürgen Moser
Publisher :
ISBN 13 :
Total Pages : 87 pages
Book Rating : 4.:/5 (118 download)
Download or read book Lectures on Hamiltonian Systems written by Jürgen Moser and published by . This book was released on 1968 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Walter T. Kyner
Publisher :
ISBN 13 : 9780608092034
Total Pages : 31 pages
Book Rating : 4.0/5 (92 download)
Download or read book Lectures on Hamiltonian Systems written by Walter T. Kyner and published by . This book was released on with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
