Àâòîð: Efstathiou Konstantinos Íàçâàíèå: Metamorphoses of Hamiltonian Systems with Symmetries ISBN: 354024316X ISBN-13(EAN): 9783540243168 Èçäàòåëüñòâî: Springer Ðåéòèíã: Öåíà: 4037 ð. Íàëè÷èå íà ñêëàäå: Ïîñòàâêà ïîä çàêàç.
Îïèñàíèå: Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.
Îïèñàíèå: Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006.
Îïèñàíèå: Offers collected notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. This title covers many aspects of the modern theory of the subject, including low dimensional problems and the theory of Hamiltonian systems in infinite dimensional phase space.
Îïèñàíèå: Physical laws are expressed in terms of differential equations, and classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. This work offers notes from lectures on Hamiltonian dynamical systems and their applications that were given at NATO Advanced Study Institute in Montreal.
Îïèñàíèå: An introduction to Hamiltonian mechanics of systems with gauge symmetry for graduate students and researchers in theoretical and mathematical physics.
Îïèñàíèå: Based on the method of canonical transformation of variables and the classical perturbation theory, this innovative book treats the systematic theory of symplectic mappings for Hamiltonian systems and its application to the study of the dynamics and chaos of various physical problems described by Hamiltonian systems. It develops a new, mathematically-rigorous method to construct symplectic mappings which replaces the dynamics of continuous Hamiltonian systems by the discrete ones. Applications of the mapping methods encompass the chaos theory in non-twist and non-smooth dynamical systems, the structure and chaotic transport in the stochastic layer, the magnetic field lines in magnetically confinement devices of plasmas, ray dynamics in waveguides, etc. The book is intended for postgraduate students and researches, physicists and astronomers working in the areas of plasma physics, hydrodynamics, celestial mechanics, dynamical astronomy, and accelerator physics. It should also be useful for applied mathematicians involved in analytical and numerical studies of dynamical systems.
Îïèñàíèå: Once again KAM theory is committed in the context of nearly integrable Hamiltonian systems. While elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Hence, without the need for untypical conditions or external parameters, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system. The text moves gradually from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations have to be replaced by Cantor sets. Planar singularities and their versal unfoldings are an important ingredient that helps to explain the underlying dynamics in a transparent way.
Îïèñàíèå: This book aims to familiarize the reader with the essential properties of the chaotic dynamics of Hamiltonian systems by avoiding specialized mathematical tools,
thus making it easily accessible to a broader audience of researchers and students. Unique material on the most intriguing and fascinating topics of unsolved and current problems in
contemporary chaos theory is presented. The coverage includes: separatrix chaos; properties and a description of systems with non-ergodic dynamics; the distribution of Poincare
recurrences and their role in transport theory; dynamical models of the Maxwell's Demon, the occurrence of persistent fluctuations, and a detailed discussion of their role in the problem
underlying the foundation of statistical physics; the emergence of stochastic webs in phase space and their link to space tiling with periodic (crystal type) and aperiodic (quasi-crystal
type) symmetries.
This second edition expands on pseudochaotic dynamics with weak mixing and the new phenomenon of fractional kinetics, which is crucial to the transport
properties of chaotic motion. The book is ideally suited to all those who are actively working on the problems of dynamical chaos as well as to those looking for new inspiration in this
area. It introduces the physicist to the world of Hamiltonian chaos and the mathematician to actual physical problems.
The material can also be used by graduate
students.
Îïèñàíèå: The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics.
For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work
by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in
shallow water.
Besides its obvious practical use, this theory is attractive also because it satisfies the aesthetic need in a beautiful formula which is so inherent to mathematics.
The second edition is up-to-date and differs from the first one considerably. One third of the book is completely new and the rest is refreshed and edited.
Îïèñàíèå: The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the
case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian
system with a torus symmetry.
It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction
methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity
theory, where computer algebra, in particular, Grobner basis techniques, are applied.
The readership addressed consists of advanced graduate students and researchers in
dynamical systems.
