Integrable systems in the realm of algebraic geometry / Pol Vanhaecke
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1638Langue : anglais.Éditeur : Berlin : Springer, 2001ISBN: 9783540423379.ISSN: 1617-9692.Sujet MSC : 14H70, Curves in algebraic geometry, Relationships between algebraic curves and integrable systems37J35, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K20, Dynamical system aspects of infinite-dimensional Hamiltonian and Lagrangian systems, Relations with algebraic geometry, complex analysis, and special functions
14K20, Abelian varieties and schemes, Analytic theory of abelian varieties; abelian integrals and differentialsEn-ligne : Springerlink | Zentralblatt | MathSciNet
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... This book presents in a coherent way a theory of algebraic completely integrable systems of classical mechanics in the language of algebraic geometry, giving an exposition of the main ideas, and the history of their development. The author introduces the important notion of the algebra of integrals, i.e., a set of regular functions in involution having maximal dimension and being complete. Then an integrable Hamiltonian system is defined as an affine Poisson variety with a maximal algebra of Casimirs and a complete algebra of integrals. ... (Zentralblatt)
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