Author: Daniel Benest
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 344

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Book Description

Author: J Delgado
Publisher: World Scientific
ISBN: 9814492116
Category : Science
Languages : en
Pages : 373

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Book Description
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.

Author: Vladimir Gerdjikov
Publisher: Springer
ISBN: 3540770542
Category : Science
Languages : en
Pages : 645

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Book Description
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.

Author: Ashley Ran Zhang
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
In this dissertation we consider problems around spectral analysis for differential operators and the non-linear Fourier transform. The first part centers at inverse spectral problems for canonical Hamiltonian systems on the right half-line $\R_+$. An algorithm for inverse spectral problems, based on the use of truncated Toeplitz operators, was recently provided in \cite{MP}. This algorithm explicitly recovers the Hamiltonian for periodic spectral measures with local infinite support. By using periodic measures to approximate non-periodic ones, an approach we call periodization, we are able to extend the algorithm to a broad class of non-periodic measures and obtain convergence results. The second part focuses on non-linear Fourier transform. Relations between spectral problems and questions for complex function theory provide a new approach for the study of scattering problems and non-linear Fourier transform \cite{Scatter}. In particular, non-linear Fourier transform can be viewed from the perspective of spectral problems. Results in \cite{MP, PZ} can be translated to results for non-linear Fourier transform. These translated results provide partial answers to some questions asked in \cite{T} and \cite{TT} on convergence of discrete non-linear Fourier transform.

Author: Bruno Cordani
Publisher: Springer Science & Business Media
ISBN: 0817683704
Category : Science
Languages : en
Pages : 347

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Book Description
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.

Author: Albert Fathi
Publisher: Cambridge University Press
ISBN: 1009320718
Category : Mathematics
Languages : en
Pages : 377

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Book Description
A selection of results, spanning a broad spectrum of disciplines, from the MSRI program on Hamiltonian Systems during Fall 2018.

Author: Carles Simó
Publisher: Springer Science & Business Media
ISBN: 940114673X
Category : Mathematics
Languages : en
Pages : 681

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Book Description
A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions.

Author: Benest
Publisher:
ISBN: 9780415327169
Category :
Languages : en
Pages :

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Author: Harry Dankowicz
Publisher: World Scientific
ISBN: 981449710X
Category : Science
Languages : en
Pages : 224

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Book Description
In the past hundred years investigators have learned the significance of complex behavior in deterministic systems. The potential applications of this discovery are as numerous as they are encouraging.This text clearly presents the mathematical foundations of chaotic dynamics, including methods and results at the forefront of current research. The book begins with a thorough introduction to dynamical systems and their applications. It goes on to develop the theory of regular and stochastic behavior in higher-degree-of-freedom Hamiltonian systems, covering topics such as homoclinic chaos, KAM theory, the Melnikov method, and Arnold diffusion. Theoretical discussions are illustrated by a study of the dynamics of small circumasteroidal grains perturbed by solar radiation pressure. With alternative derivations and proofs of established results substituted for those in the standard literature, this work serves as an important source for researchers, students and teachers.Skillfully combining in-depth mathematics and actual physical applications, this book will be of interest to the applied mathematician, the theoretical mechanical engineer and the dynamical astronomer alike.

Author:
Publisher: World Scientific
ISBN: 9789810244637
Category : Mathematics
Languages : en
Pages : 380

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Book Description
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.