LEADER 04357nam 22007095 450
001 9910299778503321
005 20211028142104.0
010 $a3-319-11026-8
024 7 $a10.1007/978-3-319-11026-4
035 $a(CKB)3710000000311622
035 $a(EBL)1968164
035 $a(OCoLC)908088884
035 $a(SSID)ssj0001408243
035 $a(PQKBManifestationID)11914747
035 $a(PQKBTitleCode)TC0001408243
035 $a(PQKBWorkID)11346944
035 $a(PQKB)11178496
035 $a(DE-He213)978-3-319-11026-4
035 $a(MiAaPQ)EBC1968164
035 $a(PPN)183153545
035 $a(EXLCZ)993710000000311622
100 $a20141201d2015 u| 0
101 0 $aeng
135 $aur|n|---|||||
181 $ctxt
182 $cc
183 $acr
200 10$aElementary Symplectic Topology and Mechanics$b[electronic resource] /$fby Franco Cardin
205 $a1st ed. 2015.
210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215 $a1 online resource (237 p.)
225 1 $aLecture Notes of the Unione Matematica Italiana,$x1862-9113 ;$v16
300 $aDescription based upon print version of record.
311 $a3-319-11025-X
320 $aIncludes bibliographical references.
327 $aBeginning -- Notes on Differential Geometry -- Symplectic Manifolds -- Poisson brackets environment -- Cauchy Problem for H-J equations -- Calculus of Variations and Conjugate Points -- Asymptotic Theory of Oscillating Integrals -- Lusternik-Schnirelman and Morse -- Finite Exact Reductions -- Other instances -- Bibliography.
330 $aThis is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincaré's last geometric theorem and the Arnol'd conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrödinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects.
410 0$aLecture Notes of the Unione Matematica Italiana,$x1862-9113 ;$v16
606 $aMathematical physics
606 $aDifferential geometry
606 $aCalculus of variations
606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000
606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022
606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016
615 0$aMathematical physics.
615 0$aDifferential geometry.
615 0$aCalculus of variations.
615 14$aMathematical Physics.
615 24$aDifferential Geometry.
615 24$aCalculus of Variations and Optimal Control; Optimization.
676 $a510
676 $a515.64
676 $a516.36
676 $a530.15
700 $aCardin$b Franco$4aut$4http://id.loc.gov/vocabulary/relators/aut$0722324
801 0$bMiAaPQ
801 1$bMiAaPQ
801 2$bMiAaPQ
906 $aBOOK
912 $a9910299778503321
996 $aElementary Symplectic Topology and Mechanics$91564840
997 $aUNINA