Topological Methods in the Theory of Integrable Systems

Download or read book Topological Methods in the Theory of Integrable Systems written by Alekseĭ Viktorovich Bolsinov and published by . This book was released on 2006 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.