Integrable Systems And Foliations PDF Download
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Author | : Claude Albert |
Publisher | : Springer Science & Business Media |
Total Pages | : 219 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461241340 |
Download Integrable Systems and Foliations Book in PDF, ePub and Kindle
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.
Author | : Claude Albert |
Publisher | : |
Total Pages | : 228 |
Release | : 1997-01-01 |
Genre | : |
ISBN | : 9781461241355 |
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Author | : A.V. Bolsinov |
Publisher | : CRC Press |
Total Pages | : 752 |
Release | : 2004-02-25 |
Genre | : Mathematics |
ISBN | : 0203643429 |
Download Integrable Hamiltonian Systems Book in PDF, ePub and Kindle
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,
Author | : B.L. Reinhart |
Publisher | : Springer Science & Business Media |
Total Pages | : 205 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642690157 |
Download Differential Geometry of Foliations Book in PDF, ePub and Kindle
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.
Author | : Chuu-lian Terng |
Publisher | : American Mathematical Soc. |
Total Pages | : 270 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 0821840487 |
Download Integrable Systems, Geometry, and Topology Book in PDF, ePub and Kindle
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. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. The article by Burstall gives a beautiful exposition on isothermic surfaces and theirrelations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu,and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of Yang-Mills-Higgs equations on Riemann surfaces. The article by Terng and Uhlenbeck explains the gauge equivalence of the matrix non-linear Schrödinger equation, the Schrödinger flow on Grassmanian, and the Heisenberg Feromagnetic model. The bookprovides an introduction to integrable systems and their relation to differential geometry. It is suitable for advanced graduate students and research mathematicians. Information for our distributors: Titles in this series are copublished with International Press, Cambridge, MA.
Author | : Jaume Llibre |
Publisher | : American Mathematical Soc. |
Total Pages | : 206 |
Release | : 1994 |
Genre | : Mathematics |
ISBN | : 082182581X |
Download Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations Book in PDF, ePub and Kindle
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.
Author | : Pierre Dazord |
Publisher | : Springer Science & Business Media |
Total Pages | : 318 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461397197 |
Download Symplectic Geometry, Groupoids, and Integrable Systems Book in PDF, ePub and Kindle
The papers, some of which are in English, the rest in French, in this volume are based on lectures given during the meeting of the Seminare Sud Rhodanien de Geometrie (SSRG) organized at the Mathematical Sciences Research Institute in 1989. The SSRG was established in 1982 by geometers and mathematical physicists with the aim of developing and coordinating research in symplectic geometry and its applications to analysis and mathematical physics. Among the subjects discussed at the meeting, a special role was given to the theory of symplectic groupoids, the subject of fruitful collaboration involving geometers from Berkeley, Lyon, and Montpellier.
Author | : Jaume Llibre |
Publisher | : |
Total Pages | : 206 |
Release | : 2014-08-31 |
Genre | : MATHEMATICS |
ISBN | : 9781470400903 |
Download Separatrix Surfaces and Invariant Manifolds of a Class of Integrable Hamiltonian Systems and Their Perturbations Book in PDF, ePub and Kindle
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.
Author | : A. T. Fomenko |
Publisher | : American Mathematical Society(RI) |
Total Pages | : 374 |
Release | : 1991 |
Genre | : Mathematics |
ISBN | : |
Download Topological Classification of Integrable Systems Book in PDF, ePub and Kindle
In recent years, researchers have found new topological invariants of integrable Hamiltonian systems of differential equations and have constructed a theory for their topological classification. Each paper in this important collection describes one of the "building blocks" of the theory, and several of the works are devoted to applications to specific physical equation. In particular, this collection covers the new topological obstructions to integrability, a new Morse-type theory of Bott integrals, and classification of bifurcations of the Liouville tori in integral systems. The papers collected here grew out of the research seminar "Contemporary Geometrical Methods" at Moscow University, under the guidance of A T Fomenko, V V Trofimov, and A V Bolsinov. Bringing together contributions by some of the experts in this area, this collection is the first publication to treat this theory in a comprehensive way.
Author | : Boris A. Kupershmidt |
Publisher | : World Scientific |
Total Pages | : 402 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : 9789810203160 |
Download Integrable and Superintegrable Systems Book in PDF, ePub and Kindle
Some of the most active practitioners in the field of integrable systems have been asked to describe what they think of as the problems and results which seem to be most interesting and important now and are likely to influence future directions. The papers in this collection, representing their authors' responses, offer a broad panorama of the subject as it enters the 1990's.