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Record Nr. |
UNINA9910481052303321 |
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Autore |
Gangbo Wilfrid |
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Titolo |
Differential forms on Wasserstein space and infinite-dimensional Hamiltonian systems / / Wilfrid Gangbo, Hwa Kil Kim, Tommaso Pacini |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 2010 |
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©2010 |
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ISBN |
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Descrizione fisica |
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1 online resource (77 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 211, Number 993 |
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Disciplina |
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Soggetti |
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Differential forms |
Hamiltonian systems |
Infinite-dimensional manifolds |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"Volume 211, Number 993 (third of 5 numbers)." |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""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 |
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