New Results in the Theory of Topological Classification of Integrable Systems
Title | New Results in the Theory of Topological Classification of Integrable Systems PDF eBook |
Author | A. T. Fomenko |
Publisher | American Mathematical Soc. |
Pages | 204 |
Release | 1995 |
Genre | Mathematics |
ISBN | 9780821804803 |
This collection contains new results in the topological classification of integrable Hamiltonian systems. Recently, this subject has been applied to interesting problems in geometry and topology, classical mechanics, mathematical physics, and computer geometry. This new stage of development of the theory is reflected in this collection. Among the topics covered are: classification of some types of singularities of the moment map (including non-Bott types), computation of topological invariants for integrable systems describing various problems in mechanics and mathematical physics, construction of a theory of bordisms of integrable systems, and solution of some problems of symplectic topology arising naturally within this theory. A list of unsolved problems allows young mathematicians to become quickly involved in this active area of research.
Topological Classification of Integrable Systems
Title | Topological Classification of Integrable Systems PDF eBook |
Author | A. T. Fomenko |
Publisher | American Mathematical Soc. |
Pages | 448 |
Release | 1991 |
Genre | Differential equations |
ISBN | 9780821841051 |
Integrable Hamiltonian Systems
Title | Integrable Hamiltonian Systems PDF eBook |
Author | A.V. Bolsinov |
Publisher | CRC Press |
Pages | 752 |
Release | 2004-02-25 |
Genre | Mathematics |
ISBN | 0203643429 |
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 Hamiltonian Systems
Title | Topological Classification of Integrable Hamiltonian Systems PDF eBook |
Author | A. T. Fomenko |
Publisher | |
Pages | 45 |
Release | 1988 |
Genre | |
ISBN |
Topological Methods in the Theory of Integrable Systems
Title | Topological Methods in the Theory of Integrable Systems PDF eBook |
Author | Alekseĭ Viktorovich Bolsinov |
Publisher | |
Pages | 360 |
Release | 2006 |
Genre | Mathematics |
ISBN |
This volume comprises selected papers on the subject of the topology of integrable systems theory which studies their qualitative properties, singularities and topological invariants. The aim of this volume is to develop the classification theory for integrable systems with two degrees of freedom which would allow for distinguishing such systems up to two natural equivalence relations. The first one is the equivalence of the associated foliations into Liouville tori. The second is the usual orbital equivalence. Also, general methods of classification theory are applied to the classical integrable problems in rigid body dynamics. In addition, integrable geodesic flows on two-dimensional surfaces are analysed from the viewpoint of the topology of integrable systems.
Symplectic Geometry
Title | Symplectic Geometry PDF eBook |
Author | A.T. Fomenko |
Publisher | CRC Press |
Pages | 488 |
Release | 1995-11-30 |
Genre | Mathematics |
ISBN | 9782881249013 |
Integrable and Superintegrable Systems
Title | Integrable and Superintegrable Systems PDF eBook |
Author | Boris A. Kupershmidt |
Publisher | World Scientific |
Pages | 402 |
Release | 1990 |
Genre | Mathematics |
ISBN | 9789810203160 |
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.