Hamiltonian Systems And Fourier Analysis
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Hamiltonian Systems And Fourier Analysis
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Author : Daniel Benest
language : en
Publisher:
Release Date : 2005
Hamiltonian Systems And Fourier Analysis written by Daniel Benest and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Celestial mechanics categories.
Geography Of Order And Chaos In Mechanics
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Author : Bruno Cordani
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-29
Geography Of Order And Chaos In Mechanics written by Bruno Cordani 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 2012-09-29 with Science categories.
This original monograph aims to explore the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces. With both analytic and numerical methods, the book studies several of these systems—including for example the hydrogen atom or the solar system, with the associated Arnold web—through modern tools such as the frequency modified fourier transform, wavelets, and the frequency modulation indicator. Meanwhile, it draws heavily on the more standard KAM and Nekhoroshev theorems. Geography of Order and Chaos in Mechanics will be a valuable resource for professional researchers and certain advanced undergraduate students in mathematics and physics, but mostly will be an exceptional reference for Ph.D. students with an interest in perturbation theory.
Hamiltonian Systems And Celestial Mechanics
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Author : J Delgado
language : en
Publisher: World Scientific
Release Date : 2000-10-09
Hamiltonian Systems And Celestial Mechanics written by J Delgado and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-09 with Science categories.
This volume is an outgrowth of the Third International Symposium on Hamiltonian Systems and Celestial Mechanics. The main topics are Arnold diffusion, central configurations, singularities in few-body problems, billiards, area-preserving maps, and geometrical mechanics. All papers in the volume went through the refereeing process typical of a mathematical research journal. Contents:The Rhomboidal Charged Four Body Problem (F Alfaro & E Pérez-Chavela)Planetary Rings with Shepherds (L Benet & T H Seligman)Low Reynolds Number Swimming in Two Dimensions (A Cherman et al.)2-Dimensional Invariant Tori for the Spatial Isosceles 3-Body Problem (M Corbera & J Llibre)The Global Flow for the Synodical Spatial Kepler Problem (M P Dantas & J Llibre)Unbounded Growth of Energy in Periodic Perturbations of Geodesic Flows of the Torus (A Delshams et al.)Splitting and Melnikov Potentials in Hamiltonian Systems (A Delshams & P Gutiérrez)Infinity Manifolds of Cubic Polynomial Hamiltonian Vector Fields with 2 Degrees of Freedom (M Falconi et al.)Relativistic Corrections to Elementary Galilean Dynamics and Deformations of Poisson Brackets (R Flores-Espinoza & Y M Vorobjev)Heteroclinic Phenomena in the Sitnikov Problem (A García & E Pérez-Chavela)Doubly-Symmetric Periodic Solutions of Hill's Lunar Problem (R C Howison & K R Meyer)On Practical Stability Regions for the Motion of a Small Particle Close to the Equilateral Points of the Real Earth-Moon System (À Jorba)Variational Methods for Quasi-Periodic Solutions of Partial Differential Equations (R de la Llave)The Splitting of Invariant Lagrangian Submanifolds: Geometry and Dynamics (J-P Marco)Cross-Sections in the Planar N-Body Problem (C McCord)Existence of an Additional First Integral and Completeness of the Flow for Hamiltonian Vector Fields (J Muciño-Raymundo)Simplification of Perturbed Hamiltonians Through Lie Transformations (J Palacián & P Yanguas)Linear Stability in the 1 + N-Gon Relative Equilibrium (G E Roberts)Analytic Continuation of Circular and Elliptic Kepler Motion to the General 3-Body Problem (J Soler)The Phase Space of Finite Systems (K B Wolf et al.) Readership: Students and researchers in mathematics and nonlinear dynamics. Keywords:Charged Four Body Problem;Low Reynolds Number;Relativistic Corrections;Sitnikov Problem;Hill's Lunar Problem;Invariant Lagrangian Submanifolds;Planar N-Body Problem;Elliptic Kepler Motion
Integrable Hamiltonian Hierarchies
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Author : Vladimir Gerdjikov
language : en
Publisher: Springer
Release Date : 2008-12-02
Integrable Hamiltonian Hierarchies written by Vladimir Gerdjikov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-02 with Science categories.
This book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies.
Resonance And Bifurcation To Chaos In Pendulum
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Author : Luo Albert C J
language : en
Publisher: World Scientific
Release Date : 2017-12-15
Resonance And Bifurcation To Chaos In Pendulum written by Luo Albert C J and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-15 with Science categories.
A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system. This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum. Contents: Resonance and Hamiltonian ChaosHamiltonian Chaos in PendulumParametric Chaos in PendulumNonlinear Discrete SystemsPeriodic Flows in Continuous SystemsPeriodic Motions to Chaos in Pendulum Readership: Researchers and academics in the field of mathematics. Keywords: Mathematics;Resonance: Bifurcation;Chaos in Pendulum;Nonlinear Science, Chaos & Dynamical SystemsReview:0
Multiphase Averaging For Classical Systems
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Author : P. Lochak
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Multiphase Averaging For Classical Systems written by P. Lochak 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 2012-12-06 with Mathematics categories.
In the past several decades many significant results in averaging for systems of ODE's have been obtained. These results have not attracted a tention in proportion to their importance, partly because they have been overshadowed by KAM theory, and partly because they remain widely scattered - and often untranslated - throughout the Russian literature. The present book seeks to remedy that situation by providing a summary, including proofs, of averaging and related techniques for single and multiphase systems of ODE's. The first part of the book surveys most of what is known in the general case and examines the role of ergodicity in averaging. Stronger stability results are then obtained for the special case of Hamiltonian systems, and the relation of these results to KAM Theory is discussed. Finally, in view of their close relation to averaging methods, both classical and quantum adiabatic theorems are considered at some length. With the inclusion of nine concise appendices, the book is very nearly self-contained, and should serve the needs of both physicists desiring an accessible summary of known results, and of mathematicians seeing an introduction to current areas of research in averaging.
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 Mechanics
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Author : John Seimenis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Hamiltonian Mechanics written by John Seimenis 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 2013-11-11 with Science categories.
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.
Hamiltonian Systems And Celestial Mechanics
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Author :
language : en
Publisher: World Scientific
Release Date : 2000
Hamiltonian Systems And Celestial Mechanics written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This volume is an outgrowth of the Third International Symposium on Hamiltonian Systems and Celestial Mechanics. The main topics are Arnold diffusion, central configurations, singularities in few-body problems, billiards, area-preserving maps, and geometrical mechanics. All papers in the volume went through the refereeing process typical of a mathematical research journal.
Semiclassical Analysis For Diffusions And Stochastic Processes
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Author : Vassili N. Kolokoltsov
language : en
Publisher: Springer
Release Date : 2007-12-03
Semiclassical Analysis For Diffusions And Stochastic Processes written by Vassili N. Kolokoltsov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-03 with Mathematics categories.
The monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition probabilities of various Markov processes. These include (i) diffusions (in particular,degenerate diffusions), (ii) more general jump-diffusions, especially stable jump-diffusions driven by stable Lévy processes, (iii) complex stochastic Schrödinger equations which correspond to models of quantum open systems. The main results of the book concern the existence, two-sided estimates, path integral representation, and small time and semiclassical asymptotics for the Green functions (or fundamental solutions) of these equations, which represent the transition probability densities of the corresponding random process. The boundary value problem for Hamiltonian systems and some spectral asymptotics ar also discussed. Readers should have an elementary knowledge of probability, complex and functional analysis, and calculus.