A Geometric Mechanism For Diffusion In Hamiltonian Systems Overcoming The Large Gap Problem Heuristics And Rigorous Verification On A Model
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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.
Relatively Hyperbolic Groups Intrinsic Geometry Algebraic Properties And Algorithmic Problems
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Author : Denis V. Osin
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Relatively Hyperbolic Groups Intrinsic Geometry Algebraic Properties And Algorithmic Problems written by Denis V. Osin 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.
In this the authors obtain an isoperimetric characterization of relatively hyperbolicity of a groups with respect to a collection of subgroups. This allows them to apply classical combinatorial methods related to van Kampen diagrams to obtain relative analogues of some well-known algebraic and geometric properties of ordinary hyperbolic groups. There is also an introduction and study of the notion of a relatively quasi-convex subgroup of a relatively hyperbolic group and solve somenatural algorithmic problems.
Kam Story The A Friendly Introduction To The Content History And Significance Of Classical Kolmogorov Arnold Moser Theory
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Author : H Scott Dumas
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-02-28
Kam Story The A Friendly Introduction To The Content History And Significance Of Classical Kolmogorov Arnold Moser Theory 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.
Betti Numbers Of The Moduli Space Of Rank 3 Parabolic Higgs Bundles
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Author : Oscar García-Prada
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Betti Numbers Of The Moduli Space Of Rank 3 Parabolic Higgs Bundles written by Oscar García-Prada 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 2007 with Mathematics categories.
Parabolic Higgs bundles on a Riemann surface are of interest for many reasons, one of them being their importance in the study of representations of the fundamental group of the punctured surface in the complex general linear group. in this paper the authors calculate the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles with fixed and non-fixed determinant, using Morse theory. A key point is that certain critical submanifolds of the Morse function can be identified with moduli spaces of parabolic triples. These moduli spaces come in families depending on a real parameter and the authors carry out a careful analysis of them by studying their variation with this parameter. Thus the authors obtain in particular information about the topology of the moduli spaces of parabolic triples for the value of the parameter relevant to the study of parabolic Higgs bundles. The remaining critical submanifolds are also described: one of them is the moduli space of parabolic bundles, while the rem
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.
Handbook Of Dynamical Systems
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Author : H. Broer
language : en
Publisher: Elsevier
Release Date : 2010-11-10
Handbook Of Dynamical Systems written by H. Broer and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-10 with Mathematics categories.
In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. - Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems - Highlights developments that are the foundation for future research in this field - Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems
New Frontiers Of Celestial Mechanics Theory And Applications
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Author : Giulio Baù
language : en
Publisher: Springer Nature
Release Date : 2023-02-09
New Frontiers Of Celestial Mechanics Theory And Applications written by Giulio Baù and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-09 with Science categories.
This volume contains the detailed text of the major lectures delivered during the I-CELMECH Training School 2020 held in Milan (Italy). The school aimed to present a contemporary review of recent results in the field of celestial mechanics, with special emphasis on theoretical aspects. The stability of the Solar System, the rotations of celestial bodies and orbit determination, as well as the novel scientific needs raised by the discovery of exoplanetary systems, the management of the space debris problem and the modern space mission design are some of the fundamental problems in the modern developments of celestial mechanics. This book covers different topics, such as Hamiltonian normal forms, the three-body problem, the Euler (or two-centre) problem, conservative and dissipative standard maps and spin-orbit problems, rotational dynamics of extended bodies, Arnold diffusion, orbit determination, space debris, Fast Lyapunov Indicators (FLI), transit orbits and answer to a crucial question, how did Kepler discover his celebrated laws? Thus, the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.
A Categorical Approach To Imprimitivity Theorems For C Dynamical Systems
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Author : Siegfried Echterhoff
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
A Categorical Approach To Imprimitivity Theorems For C Dynamical Systems written by Siegfried Echterhoff 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.
It has become apparent that studying the representation theory and structure of crossed-product C*-algebras requires imprimitivity theorems. This monograph shows that the imprimitivity theorem for reduced algebras, Green's imprimitivity theorem for actions of groups, and Mansfield's imprimitivity theorem for coactions of groups can all be understoo