Integrable Systems in the realm of Algebraic Geometry
Vanhaecke, Pol.
Integrable Systems in the realm of Algebraic Geometry [electronic resource] / by Pol Vanhaecke. - Second Edition. - XII, 264 p. online resource. - Lecture Notes in Mathematics, 1638 0075-8434 ; . - Lecture Notes in Mathematics, 1638 .
Introduction -- Integrable Hamiltonian systems on affine Poisson varietie: Affine Poisson varieties and their morphisms; Integrable Hamiltonian systems and their morphisms; Integrable Hamiltonian systems on other spaces -- Integrable Hamiltonian systems and symmetric products of curves: The systems and their integrability; The geometry of the level manifolds -- Interludium: the geometry of Abelian varieties: Divisors and line bundles; Abelian varieties; Jacobi varieties; Abelian surfaces of type (1,4) -- Algebraic completely integrable Hamiltonian systems: A.c.i. systems; Painlev analysis for a.c.i. systems; The linearization of two-dimensional a.c.i. systems; Lax equations -- The Mumford systems: Genesis; Multi-Hamiltonian structure and symmetries; The odd and the even Mumford systems; The general case -- Two-dimensional a.c.i. systems and applications: The genus two Mumford systems; Application: generalized Kummersurfaces; The Garnier potential; An integrable geodesic flow on SO(4);...
9783540445760
10.1007/3-540-44576-5 doi
Differentiable dynamical systems.
Global analysis.
Geometry, algebraic.
Dynamical Systems and Ergodic Theory.
Global Analysis and Analysis on Manifolds.
Algebraic Geometry.
Theoretical, Mathematical and Computational Physics.
QA313
515.39 515.48
Integrable Systems in the realm of Algebraic Geometry [electronic resource] / by Pol Vanhaecke. - Second Edition. - XII, 264 p. online resource. - Lecture Notes in Mathematics, 1638 0075-8434 ; . - Lecture Notes in Mathematics, 1638 .
Introduction -- Integrable Hamiltonian systems on affine Poisson varietie: Affine Poisson varieties and their morphisms; Integrable Hamiltonian systems and their morphisms; Integrable Hamiltonian systems on other spaces -- Integrable Hamiltonian systems and symmetric products of curves: The systems and their integrability; The geometry of the level manifolds -- Interludium: the geometry of Abelian varieties: Divisors and line bundles; Abelian varieties; Jacobi varieties; Abelian surfaces of type (1,4) -- Algebraic completely integrable Hamiltonian systems: A.c.i. systems; Painlev analysis for a.c.i. systems; The linearization of two-dimensional a.c.i. systems; Lax equations -- The Mumford systems: Genesis; Multi-Hamiltonian structure and symmetries; The odd and the even Mumford systems; The general case -- Two-dimensional a.c.i. systems and applications: The genus two Mumford systems; Application: generalized Kummersurfaces; The Garnier potential; An integrable geodesic flow on SO(4);...
9783540445760
10.1007/3-540-44576-5 doi
Differentiable dynamical systems.
Global analysis.
Geometry, algebraic.
Dynamical Systems and Ergodic Theory.
Global Analysis and Analysis on Manifolds.
Algebraic Geometry.
Theoretical, Mathematical and Computational Physics.
QA313
515.39 515.48