Integrable Systems And Foliations
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Integrable Systems And Foliations
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Author : Claude Albert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integrable Systems And Foliations written by Claude Albert 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.
The articles in this volume are an outgrowth of a colloquium "Systemes Integrables et Feuilletages," which was held in honor of the sixtieth birthday of Pierre Molino. The topics cover the broad range of mathematical areas which were of keen interest to Molino, namely, integral systems and more generally symplectic geometry and Poisson structures, foliations and Lie transverse structures, transitive structures, and classification problems.
Integrable Systems And Foliations
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Author : Claude Albert
language : en
Publisher:
Release Date : 1997-01-01
Integrable Systems And Foliations written by Claude Albert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with categories.
Differential Geometry Of Foliations
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Author : B.L. Reinhart
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Differential Geometry Of Foliations written by B.L. Reinhart 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.
Whoever you are! How can I but offer you divine leaves . . . ? Walt Whitman The object of study in modern differential geometry is a manifold with a differ ential structure, and usually some additional structure as well. Thus, one is given a topological space M and a family of homeomorphisms, called coordinate sys tems, between open subsets of the space and open subsets of a real vector space V. It is supposed that where two domains overlap, the images are related by a diffeomorphism, called a coordinate transformation, between open subsets of V. M has associated with it a tangent bundle, which is a vector bundle with fiber V and group the general linear group GL(V). The additional structures that occur include Riemannian metrics, connections, complex structures, foliations, and many more. Frequently there is associated to the structure a reduction of the group of the tangent bundle to some subgroup G of GL(V). It is particularly pleasant if one can choose the coordinate systems so that the Jacobian matrices of the coordinate transformations belong to G. A reduction to G is called a G-structure, which is called integrable (or flat) if the condition on the Jacobians is satisfied. The strength of the integrability hypothesis is well-illustrated by the case of the orthogonal group On. An On-structure is given by the choice of a Riemannian metric, and therefore exists on every smooth manifold.
Separatrix Surfaces And Invariant Manifolds Of A Class Of Integrable Hamiltonian Systems And Their Perturbations
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Author : Jaume Llibre
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Separatrix Surfaces And Invariant Manifolds Of A Class Of Integrable Hamiltonian Systems And Their Perturbations written by Jaume Llibre 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 1994 with Mathematics categories.
This work presents a study of the foliations of the energy levels of a class of integrable Hamiltonian systems by the sets of constant energy and angular momentum. This includes a classification of the topological bifurcations and a dynamical characterization of the critical leaves (separatrix surfaces) of the foliation. Llibre and Nunes then consider Hamiltonian perturbations of this class of integrable Hamiltonians and give conditions for the persistence of the separatrix structure of the foliations and for the existence of transversal ejection-collision orbits of the perturbed system. Finally, they consider a class of non-Hamiltonian perturbations of a family of integrable systems of the type studied earlier and prove the persistence of 'almost all' the tori and cylinders that foliate the energy levels of the unperturbed system as a consequence of KAM theory.
Separatrix Surfaces And Invariant Manifolds Of A Class Of Integrable Hamiltonian Systems And Their Perturbations
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Author : Jaume Llibre
language : en
Publisher:
Release Date : 2014-08-31
Separatrix Surfaces And Invariant Manifolds Of A Class Of Integrable Hamiltonian Systems And Their Perturbations written by Jaume Llibre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-31 with MATHEMATICS categories.
This work presents a study of the foliations of the energy levels of a class of integrable Hamiltonian systems by the sets of constant energy and angular momentum. This includes a classification of the topological bifurcations and a dynamical characterization of the criticalleaves (separatrix surfaces) of the foliation. Llibre and Nunes then consider Hamiltonain perturbations of this class of integrable Hamiltonians and give conditions for the persistence of the separatrix structure of the foliations and for the existence of transversal ejection-collision orbits of the perturbed system. Finally, they consider a class of non-Hamiltonian perturbations of a family of integrable systems of the type studied earlier and prove the persistence of almost all the tori and cylinders that foliate the energy levels of the unperturbed system as a consequence of KAM theory.
Integrable Systems Geometry And Topology
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Author : Chuu-lian Terng
language : en
Publisher: American Mathematical Soc.
Release Date :
Integrable Systems Geometry And Topology written by Chuu-lian Terng 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 articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. The article by Burstall gives a beautiful exposition on isothermic surfaces and the
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,
Topological Classification Of Integrable Systems
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Author : A. T. Fomenko
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Topological Classification Of Integrable Systems written by A. T. Fomenko 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 1991 with Differential equations categories.
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.
Integrable Systems
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Author : Jean Louis Verdier
language : en
Publisher: Springer Science & Business Media
Release Date : 1993
Integrable Systems written by Jean Louis Verdier 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 1993 with Mathematics categories.
This book contains fifteen articles by eminent specialists in the theory of completely integrable systems, bringing together the diverse approaches to classical and quantum integrable systems and covering the principal current research developments.