03593nam 22007695 450 99646677110331620211217142159.03-540-40985-810.1007/978-3-540-40985-4(CKB)1000000000231237(SSID)ssj0000325819(PQKBManifestationID)11285614(PQKBTitleCode)TC0000325819(PQKBWorkID)10253540(PQKB)11627925(DE-He213)978-3-540-40985-4(MiAaPQ)EBC6298155(MiAaPQ)EBC5591743(Au-PeEL)EBL5591743(OCoLC)55670694(PPN)155205366(EXLCZ)99100000000023123720121227d2004 u| 0engurnn#008mamaatxtccrThe Principle of Least Action in Geometry and Dynamics[electronic resource] /by Karl Friedrich Siburg1st ed. 2004.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2004.1 online resource (XII, 132 p.)Lecture Notes in Mathematics,0075-8434 ;1844Bibliographic Level Mode of Issuance: Monograph3-540-21944-7 Includes bibliographical references and index.Aubry-Mather Theory -- Mather-Mané Theory -- The Minimal Action and Convex Billiards -- The Minimal Action Near Fixed Points and Invariant Tori -- The Minimal Action and Hofer's Geometry -- The Minimal Action and Symplectic Geometry -- References -- Index.New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards, length spectrum, Hofer geometry, modern symplectic geometry). Thus, topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mather’s minimal action functional. The level is for graduate students onwards, but also for researchers in any of the subjects touched in the book.Lecture Notes in Mathematics,0075-8434 ;1844DynamicsErgodic theoryDifferential geometryGlobal analysis (Mathematics)Manifolds (Mathematics)Dynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XDifferential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Global Analysis and Analysis on Manifoldshttps://scigraph.springernature.com/ontologies/product-market-codes/M12082Dynamics.Ergodic theory.Differential geometry.Global analysis (Mathematics).Manifolds (Mathematics).Dynamical Systems and Ergodic Theory.Differential Geometry.Global Analysis and Analysis on Manifolds.53037J05msc53D35msc58E30mscSiburg Karl Friedrichauthttp://id.loc.gov/vocabulary/relators/aut283702MiAaPQMiAaPQMiAaPQBOOK996466771103316Principle of least action in geometry and dynamics262679UNISA