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Integrable Systems in the Realm of Algebraic Geometry by Pol Vanhaecke
English | PDF | 2001 | 78 Pages | ISBN : 3540423370 | 95.3 MB
This book treats the general theory of Poisson structures and integrable systems on affine varieties in a systematic way. Special attention is drawn to algebraic completely integrable systems. Several integrable systems are constructed and studied in detail and a few applications of integrable systems to algebraic geometry are worked out. In the second edition some of the concepts in Poisson geometry are clarified by introducting Poisson cohomology; the Mumford systems are constructed from the algebra of pseudo-differential operators, which clarifies their origin; a new explanation of the multi Hamiltonian structure of the Mumford systems is given by using the loop algebra of sl(2); and finally Goedesic flow on SO(4) is added to illustrate the linearizatin algorith and to give another application of integrable systems to algebraic geometry.
This book treats the general theory of Poisson structures and integrable systems on affine varieties in a systematic way. Special attention is drawn to algebraic completely integrable systems. Several integrable systems are constructed and studied in detail and a few applications of integrable systems to algebraic geometry are worked out. In the second edition some of the concepts in Poisson geometry are clarified by introducting Poisson cohomology; the Mumford systems are constructed from the algebra of pseudo-differential operators, which clarifies their origin; a new explanation of the multi Hamiltonian structure of the Mumford systems is given by using the loop algebra of sl(2); and finally Goedesic flow on SO(4) is added to illustrate the linearizatin algorith and to give another application of integrable systems to algebraic geometry.
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