Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems / / Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini
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| Autore: |
Gangbo Wilfrid
|
| Titolo: |
Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems / / Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini
|
| Pubblicazione: | Providence, Rhode Island : , : American Mathematical Society, , 2010 |
| ©2010 | |
| Descrizione fisica: | 1 online resource (77 p.) |
| Disciplina: | 515/.39 |
| Soggetto topico: | Differential forms |
| Hamiltonian systems | |
| Infinite-dimensional manifolds | |
| Soggetto genere / forma: | Electronic books. |
| Persona (resp. second.): | KimHwa Kil |
| PaciniTommaso <1971-> | |
| Note generali: | "Volume 211, Number 993 (third of 5 numbers)." |
| Nota di bibliografia: | Includes bibliographical references. |
| Nota di contenuto: | ""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"" | |
| Titolo autorizzato: | Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems |
| ISBN: | 1-4704-0610-1 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910481052303321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Memoirs of the American Mathematical Society ; ; Volume 211, Number 993.