03599nam 2200613 450 991078886610332120170822144458.01-4704-0610-1(CKB)3360000000465177(EBL)3114201(SSID)ssj0000888884(PQKBManifestationID)11483286(PQKBTitleCode)TC0000888884(PQKBWorkID)10865361(PQKB)11786564(MiAaPQ)EBC3114201(RPAM)16646796(PPN)195418824(EXLCZ)99336000000046517720150417h20102010 uy 0engur|n|---|||||txtccrDifferential forms on Wasserstein space and infinite-dimensional Hamiltonian systems /Wilfrid Gangbo, Hwa Kil Kim, Tommaso PaciniProvidence, Rhode Island :American Mathematical Society,2010.©20101 online resource (77 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 211, Number 993"Volume 211, Number 993 (third of 5 numbers)."0-8218-4939-5 Includes bibliographical references.""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""""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""""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""Memoirs of the American Mathematical Society ;Volume 211, Number 993.Differential formsHamiltonian systemsInfinite-dimensional manifoldsDifferential forms.Hamiltonian systems.Infinite-dimensional manifolds.515/.39Gangbo Wilfrid41092Kim Hwa KilPacini Tommaso1971-MiAaPQMiAaPQMiAaPQBOOK9910788866103321Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems3864207UNINA