LEADER 03568nam 22007695 450 001 9910144618603321 005 20211217142159.0 010 $a3-540-40985-8 024 7 $a10.1007/978-3-540-40985-4 035 $a(CKB)1000000000231237 035 $a(SSID)ssj0000325819 035 $a(PQKBManifestationID)11285614 035 $a(PQKBTitleCode)TC0000325819 035 $a(PQKBWorkID)10253540 035 $a(PQKB)11627925 035 $a(DE-He213)978-3-540-40985-4 035 $a(MiAaPQ)EBC6298155 035 $a(MiAaPQ)EBC5591743 035 $a(Au-PeEL)EBL5591743 035 $a(OCoLC)55670694 035 $a(PPN)155205366 035 $a(EXLCZ)991000000000231237 100 $a20121227d2004 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe Principle of Least Action in Geometry and Dynamics /$fby Karl Friedrich Siburg 205 $a1st ed. 2004. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2004. 215 $a1 online resource (XII, 132 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1844 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-21944-7 320 $aIncludes bibliographical references and index. 327 $aAubry-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. 330 $aNew variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards, length spectrum, Hofer geometry, modern symplectic geometry). Thus, topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mather?s minimal action functional. The level is for graduate students onwards, but also for researchers in any of the subjects touched in the book. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1844 606 $aDynamics 606 $aErgodic theory 606 $aGeometry, Differential 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aGeometry, Differential. 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 14$aDynamical Systems and Ergodic Theory. 615 24$aDifferential Geometry. 615 24$aGlobal Analysis and Analysis on Manifolds. 676 $a530 686 $a37J05$2msc 686 $a53D35$2msc 686 $a58E30$2msc 700 $aSiburg$b Karl Friedrich$4aut$4http://id.loc.gov/vocabulary/relators/aut$0283702 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144618603321 996 $aPrinciple of least action in geometry and dynamics$9262679 997 $aUNINA