Symmetries Topology And Resonances In Hamiltonian Mechanics PDF Download
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Author | : Valerij V. Kozlov |
Publisher | : Springer Science & Business Media |
Total Pages | : 390 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642783937 |
Download Symmetries, Topology and Resonances in Hamiltonian Mechanics Book in PDF, ePub and Kindle
John Hornstein has written about the author's theorem on nonintegrability of geodesic flows on closed surfaces of genus greater than one: "Here is an example of how differential geometry, differential and algebraic topology, and Newton's laws make music together" (Amer. Math. Monthly, November 1989). Kozlov's book is a systematic introduction to the problem of exact integration of equations of dynamics. The key to the solution is to find nontrivial symmetries of Hamiltonian systems. After Poincaré's work it became clear that topological considerations and the analysis of resonance phenomena play a crucial role in the problem on the existence of symmetry fields and nontrivial conservation laws.
Author | : Valerij V. Kozlov |
Publisher | : |
Total Pages | : 396 |
Release | : 1995-12-12 |
Genre | : |
ISBN | : 9783642783944 |
Download Symmetries, Topology and Resonances in Hamiltonian Mechanics Book in PDF, ePub and Kindle
Author | : John Seimenis |
Publisher | : Springer Science & Business Media |
Total Pages | : 417 |
Release | : 2013-11-11 |
Genre | : Science |
ISBN | : 1489909648 |
Download Hamiltonian Mechanics Book in PDF, ePub and Kindle
This volume contains invited papers and contributions delivered at the International Conference on Hamiltonian Mechanics: Integrability and Chaotic Behaviour, held in Tornn, Poland during the summer of 1993. The conference was supported by the NATO Scientific and Environmental Affairs Division as an Advanced Research Workshop. In fact, it was the first scientific conference in all Eastern Europe supported by NATO. The meeting was expected to establish contacts between East and West experts as well as to study the current state of the art in the area of Hamiltonian Mechanics and its applications. I am sure that the informal atmosphere of the city of Torun, the birthplace of Nicolaus Copernicus, stimulated many valuable scientific exchanges. The first idea for this cnference was carried out by Prof Andrzej J. Maciejewski and myself, more than two years ago, during his visit in Greece. It was planned for about forty well-known scientists from East and West. At that time participation of a scientist from Eastern Europe in an Organising Committee of a NATO Conference was not allowed. But always there is the first time. Our plans for such a "small" conference, as a first attempt in the new European situation -the Europe without borders -quickly passed away. The names of our invited speakers, authorities in their field, were a magnet for many colleagues from all over the world.
Author | : Jerrold E. Marsden |
Publisher | : Springer Science & Business Media |
Total Pages | : 593 |
Release | : 2013-03-19 |
Genre | : Science |
ISBN | : 0387217924 |
Download Introduction to Mechanics and Symmetry Book in PDF, ePub and Kindle
A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available.
Author | : Konstantinos Efstathiou |
Publisher | : Springer Science & Business Media |
Total Pages | : 164 |
Release | : 2005 |
Genre | : Hamiltonian systems |
ISBN | : 9783540243168 |
Download Metamorphoses of Hamiltonian Systems with Symmetries Book in PDF, ePub and Kindle
Author | : G. Haller |
Publisher | : Springer Science & Business Media |
Total Pages | : 444 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461215080 |
Download Chaos Near Resonance Book in PDF, ePub and Kindle
A unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, the book develops a general finite dimensional theory of homoclinic jumping, illustrating it with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics.
Author | : Giampaolo Cicogna |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 1999-10-19 |
Genre | : Language Arts & Disciplines |
ISBN | : 3540659048 |
Download Symmetry and Perturbation Theory in Nonlinear Dynamics Book in PDF, ePub and Kindle
This book deals with the theory of Poincaré--Birkhoff normal forms, studying symmetric systems in particular. Attention is focused on general Lie point symmetries, and not just on symmetries acting linearly. Some results on the simultaneous normalization of a vector field describing a dynamical system and vector fields describing its symmetry are presented and a perturbative approach is also used. Attention is given to the problem of convergence of the normalizing transformation in the presence of symmetry, with some other extensions of the theory. The results are discussed for the general case of dynamical systems and also for the specific Hamiltonian setting.
Author | : Alexey V. Borisov |
Publisher | : Springer Science & Business Media |
Total Pages | : 501 |
Release | : 2007-12-22 |
Genre | : Science |
ISBN | : 1402067445 |
Download IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence Book in PDF, ePub and Kindle
This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important.
Author | : A.V. Bolsinov |
Publisher | : CRC Press |
Total Pages | : 752 |
Release | : 2004-02-25 |
Genre | : Mathematics |
ISBN | : 0203643429 |
Download Integrable Hamiltonian Systems Book in PDF, ePub and Kindle
Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,
Author | : Hendrik W. Broer |
Publisher | : Springer |
Total Pages | : 203 |
Release | : 2009-01-25 |
Genre | : Mathematics |
ISBN | : 3540496130 |
Download Quasi-Periodic Motions in Families of Dynamical Systems Book in PDF, ePub and Kindle
This book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. Such a motion in the phase space densely fills up an invariant torus. This phenomenon is most familiar from Hamiltonian dynamics. Hamiltonian systems are well known for their use in modelling the dynamics related to frictionless mechanics, including the planetary and lunar motions. In this context the general picture appears to be as follows. On the one hand, Hamiltonian systems occur that are in complete order: these are the integrable systems where all motion is confined to invariant tori. On the other hand, systems exist that are entirely chaotic on each energy level. In between we know systems that, being sufficiently small perturbations of integrable ones, exhibit coexistence of order (invariant tori carrying quasi-periodic dynamics) and chaos (the so called stochastic layers). The Kolmogorov-Arnol'd-Moser (KAM) theory on quasi-periodic motions tells us that the occurrence of such motions is open within the class of all Hamiltonian systems: in other words, it is a phenomenon persistent under small Hamiltonian perturbations. Moreover, generally, for any such system the union of quasi-periodic tori in the phase space is a nowhere dense set of positive Lebesgue measure, a so called Cantor family. This fact implies that open classes of Hamiltonian systems exist that are not ergodic. The main aim of the book is to study the changes in this picture when other classes of systems - or contexts - are considered.