Format:
Online-Ressource (XIV, 386 p. 11 illus, digital)
ISBN:
9783642008733
,
1282290614
,
9783642008726
,
9781282290617
Series Statement:
Abel Symposia 5
Content:
Some Canonical Structures of Cartan Planes in Jet Spaces and Applications -- Transformations of Darboux Integrable Systems -- Differential Geometric Heuristics for Riemannian Optimal Mass Transportation -- On Rank Problems for Planar Webs and Projective Structures -- Niceness Theorems -- The Polynomial Algebra and Quantizations of Electromagnetic Fields -- A Bridge Between Lie Symmetries and Galois Groups -- Focal Systems for Pfaffian Systems with Characteristics -- Hamiltonian Structures for General PDEs -- Point Classification of Second Order ODEs: Tresse Classification Revisited and Beyond -- Classification of Monge#x2013;Ampe#x00E8;re Equations -- On Nonabelian Theories and Abelian Differentials -- Geometric Aspects of the Quantization of a Rigid Body -- Shooting for the Eight -- Compatible Poisson brackets, quadratic Poisson algebras and classical -matrices -- Contact Geometry of Second Order I.
Content:
The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. Following the tradition of Monge, Abel and Lie, the scientific program emphasized the role of algebro-geometric methods, which nowadays permeate all mathematical models in natural and engineering sciences. The ideas of invariance and symmetry are of fundamental importance in the geometric approach to differential equations, with a serious impact coming from the area of integrable systems and field theories. This volume consists of original contributions and broad overview lectures of the participants of the Symposium. The papers in this volume present the modern approach to this classical subject.
Note:
Includes bibliographical references
,
Differential Equations: Geometry, Symmetries and Integrability; Some Canonical Structures of Cartan Planes in Jet Spaces and Applications; Transformations of Darboux Integrable Systems; Differential Geometric Heuristics for Riemannian Optimal Mass Transportation; On Rank Problems for Planar Webs and Projective Structures; Niceness Theorems; The Polynomial Algebra and Quantizations of Electromagnetic Fields; A Bridge Between Lie Symmetries and Galois Groups; Focal Systems for Pfaffian Systems with Characteristics; Hamiltonian Structures for General PDEs
,
Point Classification of Second Order ODEs: Tresse Classification Revisited and BeyondClassification of Monge--Ampère Equations; On Nonabelian Theories and Abelian Differentials; Geometric Aspects of the Quantization of a Rigid Body; Shooting for the Eight: A Topological Existence Proof for a Figure-Eight Orbit of the Three-Body Problem; Compatible Poisson Brackets, Quadratic Poisson Algebras and Classical r-Matrices; Contact Geometry of Second Order I;
Additional Edition:
ISBN 9783642008726
Additional Edition:
Buchausg. u.d.T. Differential equations Berlin : Springer, 2009 ISBN 9783642008726
Language:
English
Subjects:
Mathematics
Keywords:
Differentialgleichung
;
Konferenzschrift
DOI:
10.1007/978-3-642-00873-3
URL:
Volltext
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URL:
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