Hamiltonian Dynamics Theory And Applications
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Hamiltonian Dynamics Theory And Applications
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Author : CIME-EMS Summer School (
language : en
Publisher: Springer Science & Business Media
Release Date : 2005
Hamiltonian Dynamics Theory And Applications written by CIME-EMS Summer School ( and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Hamiltonian systems categories.
Hamiltonian Dynamics Theory And Applications
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Author : Giancarlo Benettin
language : en
Publisher: Springer
Release Date : 2005-01-14
Hamiltonian Dynamics Theory And Applications written by Giancarlo Benettin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-14 with Mathematics categories.
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.
Hamiltonian Dynamical Systems And Applications
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Author : Walter Craig
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-17
Hamiltonian Dynamical Systems And Applications written by Walter Craig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-17 with Mathematics categories.
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.
Hamiltonian Dynamics Theory And Applications
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Author : CIME-EMS Summer School (
language : en
Publisher: Springer Science & Business Media
Release Date : 2005
Hamiltonian Dynamics Theory And Applications written by CIME-EMS Summer School ( and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Hamiltonian systems categories.
Construction Of Mappings For Hamiltonian Systems And Their Applications
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Author : Sadrilla S. Abdullaev
language : en
Publisher: Springer
Release Date : 2006-08-02
Construction Of Mappings For Hamiltonian Systems And Their Applications written by Sadrilla S. Abdullaev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-02 with Science categories.
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.
Essentials Of Hamiltonian Dynamics
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Author : John H. Lowenstein
language : en
Publisher: Cambridge University Press
Release Date : 2012-01-19
Essentials Of Hamiltonian Dynamics written by John H. Lowenstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-19 with Science categories.
Classical dynamics is one of the cornerstones of advanced education in physics and applied mathematics, with applications across engineering, chemistry and biology. In this book, the author uses a concise and pedagogical style to cover all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods. Readers are introduced to the impressive advances in the field during the second half of the twentieth century, including KAM theory and deterministic chaos. Essential to these developments are some exciting ideas from modern mathematics, which are introduced carefully and selectively. Core concepts and techniques are discussed, together with numerous concrete examples to illustrate key principles. A special feature of the book is the use of computer software to investigate complex dynamical systems, both analytically and numerically. This text is ideal for graduate students and advanced undergraduates who are already familiar with the Newtonian and Lagrangian treatments of classical mechanics. The book is well suited to a one-semester course, but is easily adapted to a more concentrated format of one-quarter or a trimester. A solutions manual and introduction to Mathematica® are available online at www.cambridge.org/Lowenstein.
Perturbation Theory
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Author : Giuseppe Gaeta
language : en
Publisher: Springer Nature
Release Date : 2022-12-16
Perturbation Theory written by Giuseppe Gaeta and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-16 with Science categories.
This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, is devoted to the fundamentals of Perturbation Theory (PT) as well as key applications areas such as Classical and Quantum Mechanics, Celestial Mechanics, and Molecular Dynamics. Less traditional fields of application, such as Biological Evolution, are also discussed. Leading scientists in each area of the field provide a comprehensive picture of the landscape and the state of the art, with the specific goal of combining mathematical rigor, explicit computational methods, and relevance to concrete applications. New to this edition are chapters on Water Waves, Rogue Waves, Multiple Scales methods, legged locomotion, Condensed Matter among others, while all other contributions have been revised and updated. Coverage includes the theory of (Poincare’-Birkhoff) Normal Forms, aspects of PT in specific mathematical settings (Hamiltonian, KAM theory, Nekhoroshev theory, and symmetric systems), technical problems arising in PT with solutions, convergence of series expansions, diagrammatic methods, parametric resonance, systems with nilpotent real part, PT for non-smooth systems, and on PT for PDEs [write out this acronym partial differential equations]. Another group of papers is focused specifically on applications to Celestial Mechanics, Quantum Mechanics and the related semiclassical PT, Quantum Bifurcations, Molecular Dynamics, the so-called choreographies in the N-body problem, as well as Evolutionary Theory. Overall, this unique volume serves to demonstrate the wide utility of PT, while creating a foundation for innovations from a new generation of graduate students and professionals in Physics, Mathematics, Mechanics, Engineering and the Biological Sciences.
Introduction To Hamiltonian Fluid Dynamics And Stability Theory
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Author : Gordon E Swaters
language : en
Publisher: Routledge
Release Date : 2019-01-22
Introduction To Hamiltonian Fluid Dynamics And Stability Theory written by Gordon E Swaters and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-22 with Mathematics categories.
Hamiltonian fluid dynamics and stability theory work hand-in-hand in a variety of engineering, physics, and physical science fields. Until now, however, no single reference addressed and provided background in both of these closely linked subjects. Introduction to Hamiltonian Fluid Dynamics and Stability Theory does just that-offers a comprehensive introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic stability theory within the context of the Hamiltonian formalism. The author uses the example of the nonlinear pendulum-giving a thorough linear and nonlinear stability analysis of its equilibrium solutions-to introduce many of the ideas associated with the mathematical argument required in infinite dimensional Hamiltonian theory needed for fluid mechanics. He examines Andrews' Theorem, derives and develops the Charney-Hasegawa-Mima (CMH) equation, presents an account of the Hamiltonian structure of the Korteweg-de Vries (KdV) equation, and discusses the stability theory associated with the KdV soliton. The book's tutorial approach and plentiful exercises combine with its thorough presentations of both subjects to make Introduction to Hamiltonian Fluid Dynamics and Stability Theory an ideal reference, self-study text, and upper level course book.
Hamiltonian Dynamics
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Author : Gaetano Vilasi
language : en
Publisher: World Scientific
Release Date : 2001
Hamiltonian Dynamics written by Gaetano Vilasi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Science categories.
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems.As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity.As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations.
Lectures On Hyperhamiltonian Dynamics And Physical Applications
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Author : Giuseppe Gaeta
language : en
Publisher: Springer
Release Date : 2017-07-21
Lectures On Hyperhamiltonian Dynamics And Physical Applications written by Giuseppe Gaeta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-21 with Science categories.
This book provides the mathematical foundations of the theory of hyperhamiltonian dynamics, together with a discussion of physical applications. In addition, some open problems are discussed. Hyperhamiltonian mechanics represents a generalization of Hamiltonian mechanics, in which the role of the symplectic structure is taken by a hyperkähler one (thus there are three Kähler/symplectic forms satisfying quaternionic relations). This has proved to be of use in the description of physical systems with spin, including those which do not admit a Hamiltonian formulation. The book is the first monograph on the subject, which has previously been treated only in research papers.