LEADER 03602nam 2200613 450 001 9910481052303321 005 20170822144458.0 010 $a1-4704-0610-1 035 $a(CKB)3360000000465177 035 $a(EBL)3114201 035 $a(SSID)ssj0000888884 035 $a(PQKBManifestationID)11483286 035 $a(PQKBTitleCode)TC0000888884 035 $a(PQKBWorkID)10865361 035 $a(PQKB)11786564 035 $a(MiAaPQ)EBC3114201 035 $a(PPN)195418824 035 $a(EXLCZ)993360000000465177 100 $a20150417h20102010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDifferential forms on Wasserstein space and infinite-dimensional Hamiltonian systems /$fWilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2010. 210 4$dİ2010 215 $a1 online resource (77 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 211, Number 993 300 $a"Volume 211, Number 993 (third of 5 numbers)." 311 $a0-8218-4939-5 320 $aIncludes bibliographical references. 327 $a""Contents""; ""Abstract""; ""Chapter 1. Introduction""; ""Chapter 2. The topology on M and a differential calculus of curves""; ""2.1. The space of distributions""; ""2.2. The topology on M""; ""2.3. Tangent spaces and the divergence operator""; ""2.4. Analytic justification for the tangent spaces""; ""Chapter 3. The calculus of curves, revisited""; ""3.1. Embedding the geometry of RD into M""; ""3.2. The intrinsic geometry of M""; ""3.3. Embedding the geometry of M into (Cc)*""; ""3.4. Further comments""; ""Chapter 4. Tangent and cotangent bundles"" 327 $a""4.1. Push-forward operations on M and TM""""4.2. Differential forms on M""; ""4.3. Discussion""; ""Chapter 5. Calculus of pseudo differential 1-forms""; ""5.1. Green's formula for smooth surfaces and 1-forms""; ""5.2. Regularity and differentiability of pseudo 1-forms""; ""5.3. Regular forms and absolutely continuous curves""; ""5.4. Green's formula for annuli""; ""5.5. Example: 1-forms on the space of discrete measures""; ""5.6. Discussion""; ""Chapter 6. A symplectic foliation of M""; ""6.1. The group of Hamiltonian diffeomorphisms""; ""6.2. A symplectic foliation of M"" 327 $a""6.3. Algebraic properties of the symplectic distribution""""Chapter 7. The symplectic foliation as a Poisson structure""; ""7.1. Review of Poisson geometry""; ""7.2. The symplectic foliation of M, revisited""; ""Appendix A. Review of relevant notions of Differential Geometry""; ""A.1. Calculus of vector fields and differential forms""; ""A.2. Lie groups and group actions""; ""A.3. Cohomology and invariant cohomology""; ""A.4. The group of diffeomorphisms""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 211, Number 993. 606 $aDifferential forms 606 $aHamiltonian systems 606 $aInfinite-dimensional manifolds 608 $aElectronic books. 615 0$aDifferential forms. 615 0$aHamiltonian systems. 615 0$aInfinite-dimensional manifolds. 676 $a515/.39 700 $aGangbo$b Wilfrid$041092 702 $aKim$b Hwa Kil 702 $aPacini$b Tommaso$f1971- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910481052303321 996 $aDifferential forms on Wasserstein space and infinite-dimensional Hamiltonian systems$92087519 997 $aUNINA