A Geometric Mechanism For Diffusion In Hamiltonian Systems Overcoming The Large Gap Problem
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A Geometric Mechanism For Diffusion In Hamiltonian Systems Overcoming The Large Gap Problem
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Author : Amadeu Delshams
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
A Geometric Mechanism For Diffusion In Hamiltonian Systems Overcoming The Large Gap Problem written by Amadeu Delshams and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Beginning by introducing a geometric mechanism for diffusion in a prioriunstable nearly integrable dynamical systems, this book is based onthe observation that resonances, besides destroying the primary KAMtori, create secondary tori and tori of lower dimension. It argues thatthese objects created by resonances can be incorporated in transitionchains taking the place of the destroyed primary KAM tori.The authorsestablish rigorously the existence of this mechanism in a simple modelthat has been studied before. The main technique is to develop a toolkitto study, in a unified way, tori of different topologies and their invariantmanifolds, their intersections as well as shadowing properties of thesebi-asymptotic orbits. This toolkit is based on extending and unifyingstandard techniques.
A Geometric Mechanism For Diffusion In Hamiltonian Systems Overcoming The Large Gap Problem Heuristics And Rigorous Verification On A Model
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Author : Amadeu Delshams
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
A Geometric Mechanism For Diffusion In Hamiltonian Systems Overcoming The Large Gap Problem Heuristics And Rigorous Verification On A Model written by Amadeu Delshams and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Beginning by introducing a geometric mechanism for diffusion in a priori unstable nearly integrable dynamical systems. This book is based on the observation that resonances, besides destroying the primary KAM tori, create secondary tori and tori of lower dimension. It argues that these objects created by resonances can be incorporated in transition chains taking the place of the destroyed primary KAM tori.The authors establish rigorously the existence of this mechanism in a simplemodel that has been studied before. The main technique is to develop a toolkit to study, in a unified way, tori of different topologies and their invariant manifolds, their intersections as well as shadowing properties of these bi-asymptotic orbits. This toolkit is based on extending and unifyingstandard techniques. A new tool used here is the scattering map of normally hyperbolic invariant manifolds.The model considered is a one-parameter family, which for $\varepsilon = 0$ is an integrable system. We give a small number of explicit conditions the jet of order $3$ of the family that, if verified imply diffusion. The conditions are just that some explicitely constructed functionals do not vanish identically or have non-degenerate critical points, etc.An attractive feature of themechanism is that the transition chains are shorter in the places where the heuristic intuition and numerical experimentation suggests that the diffusion is strongest.
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 Systems
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Author : Albert Fathi
language : en
Publisher: Cambridge University Press
Release Date : 2024-05-31
Hamiltonian Systems written by Albert Fathi 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 2024-05-31 with Mathematics categories.
A selection of results, spanning a broad spectrum of disciplines, from the MSRI program on Hamiltonian Systems during Fall 2018.
Arnold Diffusion For Smooth Systems Of Two And A Half Degrees Of Freedom
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Author : Vadim Kaloshin
language : en
Publisher: Princeton University Press
Release Date : 2020-11-03
Arnold Diffusion For Smooth Systems Of Two And A Half Degrees Of Freedom written by Vadim Kaloshin and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-03 with Mathematics categories.
The first complete proof of Arnold diffusion—one of the most important problems in dynamical systems and mathematical physics Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. Kaloshin and Zhang follow Mather's strategy but emphasize a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, this book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.
Local And Semi Local Bifurcations In Hamiltonian Dynamical Systems
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Author : Heinz Hanßmann
language : en
Publisher: Springer
Release Date : 2006-10-18
Local And Semi Local Bifurcations In Hamiltonian Dynamical Systems written by Heinz Hanßmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-18 with Mathematics categories.
This book demonstrates that while elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Therefore, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system, absent untypical conditions or external parameters. The text moves logically from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations must be replaced by Cantor sets.
Variational Methods
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Author : Maïtine Bergounioux
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-01-11
Variational Methods written by Maïtine Bergounioux and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-11 with Mathematics categories.
With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents: Part I Second-order decomposition model for image processing: numerical experimentation Optimizing spatial and tonal data for PDE-based inpainting Image registration using phase・amplitude separation Rotation invariance in exemplar-based image inpainting Convective regularization for optical flow A variational method for quantitative photoacoustic tomography with piecewise constant coefficients On optical flow models for variational motion estimation Bilevel approaches for learning of variational imaging models Part II Non-degenerate forms of the generalized Euler・Lagrange condition for state-constrained optimal control problems The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls Controllability of Keplerian motion with low-thrust control systems Higher variational equation techniques for the integrability of homogeneous potentials Introduction to KAM theory with a view to celestial mechanics Invariants of contact sub-pseudo-Riemannian structures and Einstein・Weyl geometry Time-optimal control for a perturbed Brockett integrator Twist maps and Arnold diffusion for diffeomorphisms A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I Index
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Author :
language : en
Publisher: World Scientific
Release Date :
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 with categories.
Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures
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Author : Rajendra Bhatia
language : en
Publisher: World Scientific
Release Date : 2011-06-06
Proceedings Of The International Congress Of Mathematicians 2010 Icm 2010 In 4 Volumes Vol I Plenary Lectures And Ceremonies Vols Ii Iv Invited Lectures written by Rajendra Bhatia and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-06 with Mathematics categories.
ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.
The Kam Story
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Author : H Scott Dumas
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-02-28
The Kam Story written by H Scott Dumas and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-28 with Mathematics categories.
This is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM theory, and scientific-minded readers. Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science. The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a “breakthrough”). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory). Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it leads the reader through an accessible account of the theory and places it in its proper context in mathematics, physics, and the history of science.