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Integrable Systems in the Realm of Algebraic Geometry : Lecture Notes in Computer Science - Pol Vanhaecke

Integrable Systems in the Realm of Algebraic Geometry

Lecture Notes in Computer Science

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Published: September 2001
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I. Introduction: II. Integrable Hamiltonian systems on affine Poisson varieties: 1. Introduction.- 2. Affine Poisson varieties and their morphisms.- 3. Integrable Hamiltonian systems and their morphisms.- 4. Integrable Hamiltonian systems on other spaces.- III. Integrable Hamiltonian systems and symmetric products of curves: 1. Introduction.- 2. The systems and their integrability.- 3. The geometry of the level manifolds.- IV. Interludium: the geometry of Abelian varieties 1. Introduction.- 2. Divisors and line bundles.- 3. Abelian varieties.- 4. Jacobi varieties.- 5. Abelian surfaces of type (1,4).- V. Algebraic completely integrable Hamiltonian systems: 1. Introduction.- 2. A.c.i. systems.- 3. Painlev analysis for a.c.i. systems.- 4. The linearization of two-dimensional a.c.i. systems.- 5. Lax equations.- VI. The Mumford systems 1. Introduction.- 2. Genesis.- 3. Multi-Hamiltonian structure and symmetries.- 4. The odd and the even Mumford systems.- 5. The general case.- VII. Two-dimensional a.c.i. systems and applications 1. Introduction.- 2. The genus two Mumford systems.- 3. Application: generalized Kummersurfaces.- 4. The Garnier potential.- 5. An integrable geodesic flow on SO(4).- 6. The Hnon-Heiles hierarchy.- 7. The Toda lattice.- References.- Index.

Introductionp. 1
Integrable Hamiltonian systems on affine Poisson varietiesp. 17
Introductionp. 17
Affine Poisson varieties and their morphismsp. 19
Integrable Hamiltonian systems and their morphismsp. 47
Integrable Hamiltonian systems on other spacesp. 65
Integrable Hamiltonian systems and symmetric products of curvesp. 71
Introductionp. 71
The systems and their integrabilityp. 73
The geometry of the level manifoldsp. 85
Interludium: the geometry of Abelian varietiesp. 97
Introductionp. 97
Divisors and line bundlesp. 99
Abelian varietiesp. 108
Jacobi varietiesp. 114
Abelian surfaces of type (1,4)p. 123
Algebraic completely integrable Hamiltonian systemsp. 127
Introductionp. 127
A.c.i. systemsp. 129
Painleve analysis for a.c.i. systemsp. 135
The linearization of two-dimensional a.c.i. systemsp. 138
Lax equationsp. 140
The Mumford systemsp. 143
Introductionp. 143
Genesisp. 145
Multi-Hamiltonian structure and symmetriesp. 155
The odd and the even Mumford systemsp. 161
The general casep. 168
Two-dimensional a.c.i. systems and applicationsp. 175
Introductionp. 175
The genus two Mumford systemsp. 177
Application: generalized Kummer surfacesp. 185
The Garnier potentialp. 196
An integrable geodesic flow on SO(4)p. 220
The Henon-Heiles hierarchyp. 230
The Toda latticep. 235
Referencesp. 243
Indexp. 253
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540423379
ISBN-10: 3540423370
Series: Lecture Notes in Computer Science
Audience: General
Format: Paperback
Language: English
Number Of Pages: 264
Published: September 2001
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.47
Weight (kg): 0.39
Edition Number: 2
Edition Type: Revised