Four Dimensional Integrable Hamiltonian Systems With Simple Singular Points Topological Aspects

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Four Dimensional Integrable Hamiltonian Systems With Simple Singular Points Topological Aspects

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Author : Lev M. Lerman
language : en
Publisher: American Mathematical Soc.
Release Date : 1998

Four Dimensional Integrable Hamiltonian Systems With Simple Singular Points Topological Aspects written by Lev M. Lerman 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 1998 with Mathematics categories.

The main topic of this book is the isoenergetic structure of the Liouville foliation generated by an integrable system with two degrees of freedom and the topological structure of the corresponding Poisson action of the group ${\mathbb R}^2$. This is a first step towards understanding the global dynamics of Hamiltonian systems and applying perturbation methods. Emphasis is placed on the topology of this foliation rather than on analytic representation. In contrast to previously published works in this area, here the authors consistently use the dynamical properties of the action to achieve their results.

Four Dimensional Integrable Hamiltonian Systems With Simple Singular Points Topological Aspects

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Author : Lev M. Lerman Ya. L. Umanskiy
language : en
Publisher: American Mathematical Soc.
Release Date :

Four Dimensional Integrable Hamiltonian Systems With Simple Singular Points Topological Aspects written by Lev M. Lerman Ya. L. Umanskiy 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 with Mathematics categories.

The main topic of this book is the isoenergetic structure of the Liouville foliation generated by an integrable system with two degrees of freedom and the topological structure of the corresponding Poisson action of the group R2. This is a first step towards understanding the global dynamics of Hamiltonian systems and applying perturbation methods. Emphasis is placed on the topology of this foliation rather than on analytic representation. In contrast to previously published works in this area, here the authors consistently use the dynamical properties of the action to achieve their results.

Geometry And Dynamics Of Integrable Systems

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Author : Alexey Bolsinov
language : en
Publisher: Birkhäuser
Release Date : 2016-10-27

Geometry And Dynamics Of Integrable Systems written by Alexey Bolsinov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-27 with Mathematics categories.

Based on lectures given at an advanced course on integrable systems at the Centre de Recerca Matemàtica in Barcelona, these lecture notes address three major aspects of integrable systems: obstructions to integrability from differential Galois theory; the description of singularities of integrable systems on the basis of their relation to bi-Hamiltonian systems; and the generalization of integrable systems to the non-Hamiltonian settings. All three sections were written by top experts in their respective fields. Native to actual problem-solving challenges in mechanics, the topic of integrable systems is currently at the crossroads of several disciplines in pure and applied mathematics, and also has important interactions with physics. The study of integrable systems also actively employs methods from differential geometry. Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mirror symmetry). As such, the book will appeal to experts with a wide range of backgrounds.

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.

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

Global Aspects Of Classical Integrable Systems

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Author : Richard H. Cushman
language : en
Publisher: Birkhäuser
Release Date : 2015-06-01

Global Aspects Of Classical Integrable Systems written by Richard H. Cushman and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-01 with Science categories.

This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.

Methods Of Qualitative Theory Of Differential Equations And Related Topics

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Author : Lev M. Lerman
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Methods Of Qualitative Theory Of Differential Equations And Related Topics written by Lev M. Lerman 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 2000 with Mathematics categories.

Dedicated to the memory of Professor E. A. Leontovich-Andronova, this book was composed by former students and colleagues who wished to mark her contributions to the theory of dynamical systems. A detailed introduction by Leontovich-Andronova's close colleague, L. Shilnikov, presents biographical data and describes her main contribution to the theory of bifurcations and dynamical systems. The main part of the volume is composed of research papers presenting the interests of Leontovich-Andronova, her students and her colleagues. Included are articles on traveling waves in coupled circle maps, bifurcations near a homoclinic orbit, polynomial quadratic systems on the plane, foliations on surfaces, homoclinic bifurcations in concrete systems, topology of plane controllability regions, separatrix cycle with two saddle-foci, dynamics of 4-dimensional symplectic maps, torus maps from strong resonances, structure of 3 degree-of-freedom integrable Hamiltonian systems, splitting separatrices in complex differential equations, Shilnikov's bifurcation for C1-smooth systems and "blue sky catastrophe" for periodic orbits.

Chaotic Dynamics And Transport In Classical And Quantum Systems

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Author : Pierre Collet
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-07-28

Chaotic Dynamics And Transport In Classical And Quantum Systems written by Pierre Collet 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 2005-07-28 with Science categories.

From the 18th to the 30th August 2003 , a NATO Advanced Study Institute (ASI) was held in Cargèse, Corsica, France. Cargèse is a nice small village situated by the mediterranean sea and the Institut d'Etudes Scientifiques de Cargese provides ? a traditional place to organize Theoretical Physics Summer Schools and Workshops * in a closed and well equiped place. The ASI was an International Summer School on "Chaotic Dynamics and Transport in Classical and Quantum Systems". The main goal of the school was to develop the mutual interaction between Physics and Mathematics concerning statistical properties of classical and quantum dynamical systems. Various experimental and numerical observations have shown new phenomena of chaotic and anomalous transport, fractal structures, chaos in physics accelerators and in cooled atoms inside atom-optics billiards, space-time chaos, fluctuations far from equilibrium, quantum decoherence etc. New theoretical methods have been developed in order to modelize and to understand these phenomena (volume preserving and ergodic dynamical systems, non-equilibrium statistical dynamics, fractional kinetics, coupled maps, space-time entropy, quantum dissipative processes etc). The school gathered a team of specialists from several horizons lecturing and discussing on the achievements, perspectives and open problems (both fundamental and applied).

Integrable Hamiltonian Systems

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Author : A.V. Bolsinov
language : en
Publisher: CRC Press
Release Date : 2004-02-25

Integrable Hamiltonian Systems written by A.V. Bolsinov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-25 with Mathematics categories.

Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,

Selected Topics In Integral Geometry

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Author : Izrail_ Moiseevich Gel_fand
language : en
Publisher: American Mathematical Soc.
Release Date : 2003-09-02

Selected Topics In Integral Geometry written by Izrail_ Moiseevich Gel_fand 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 2003-09-02 with Mathematics categories.

The miracle of integral geometry is that it is often possible to recover a function on a manifold just from the knowledge of its integrals over certain submanifolds. The founding example is the Radon transform, introduced at the beginning of the 20th century. Since then, many other transforms were found, and the general theory was developed. Moreover, many important practical applications were discovered, the best known, but by no means the only one, being to medical tomography. The present book is a general introduction to integral geometry, the first from this point of view for almost four decades. The authors, all leading experts in the field, represent one of the most influential schools in integral geometry. The book presents in detail basic examples of integral geometry problems, such as the Radon transform on the plane and in space, the John transform, the Minkowski-Funk transform, integral geometry on the hyperbolic plane and in the hyperbolic space, the horospherical transform and its relation to representations of $SL(2,\mathbb C)$, integral geometry on quadrics, etc. The study of these examples allows the authors to explain important general topics of integral geometry, such as the Cavalieri conditions, local and nonlocal inversion formulas, and overdetermined problems. Many of the results in the book were obtained by the authors in the course of their career-long work in integral geometry.