Differential Geometry and Mathematical Physics [[electronic resource] ] : Part I. Manifolds, Lie Groups and Hamiltonian Systems / / by Gerd Rudolph, Matthias Schmidt

• Autore: Rudolph Gerd
• Pubblicazione: Dordrecht : , : Springer Netherlands : , : Imprint : Springer, , 2013
• Edizione: 1st ed. 2013.
• Descrizione fisica: 1 online resource (765 p.)
• Disciplina: 515.7; 516.36
• Soggetto topico: Physics; Global analysis (Mathematics); Manifolds (Mathematics); Mechanics; Topological groups; Lie groups; Differential geometry; Mathematical Methods in Physics; Global Analysis and Analysis on Manifolds; Classical Mechanics; Topological Groups, Lie Groups; Differential Geometry
• Persona (resp. second.): SchmidtMatthias
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 1 Differentiable manifolds -- 2 Vector bundles -- 3 Vector fields -- 4 Differential forms -- 5 Lie groups -- 6 Lie group actions -- 7 Linear symplectic algebra -- 8 Symplectic geometry -- 9 Hamiltonian systems -- 10 Symmetries -- 11 Integrability -- 12 Hamilton-Jacobi theory -- References.
• Sommario/riassunto: Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
• Titolo autorizzato: Differential geometry and mathematical physics
• ISBN: 1-283-90982-0; 94-007-5345-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910736987103321
• Lo trovi qui: Univ. Federico II
• Serie: Theoretical and Mathematical Physics, . 1864-5879