Poisson algebras and convexity
| dc.contributor.advisor | Flaschka, Hermann | en_US |
| dc.contributor.author | El Hadrami, Mohamed Lemine Ould, 1962- | |
| dc.creator | El Hadrami, Mohamed Lemine Ould, 1962- | en_US |
| dc.date.accessioned | 2013-05-09T11:35:34Z | |
| dc.date.available | 2013-05-09T11:35:34Z | |
| dc.date.issued | 1996 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10150/290675 | |
| dc.description.abstract | In this dissertation, we identify a subgroup Tˢ of Dˢ(μ), the group of Sobolev symplectomorphisms of CP (n), n = 1,2 that has all the properties of a torus of a compact finite dimensional Lie group. We prove that Tˢ: (1) topologically is a submanifold of Dˢ(μ); (2) algebraically is a maximal abelian subgroup of Dˢ(μ); (3) geometrically is flat and totally geodesic. We also characterize the doubly stochastic operators on measurable spaces and use this result to extend the convexity Theorem of T. Bloch, H. Flaschka and T. Ratiu. | |
| dc.language.iso | en_US | en_US |
| dc.publisher | The University of Arizona. | en_US |
| dc.rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. | en_US |
| dc.subject | Mathematics. | en_US |
| dc.title | Poisson algebras and convexity | en_US |
| dc.type | text | en_US |
| dc.type | Dissertation-Reproduction (electronic) | en_US |
| thesis.degree.grantor | University of Arizona | en_US |
| thesis.degree.level | doctoral | en_US |
| dc.identifier.proquest | 9720631 | en_US |
| thesis.degree.discipline | Graduate College | en_US |
| thesis.degree.discipline | Mathematics | en_US |
| thesis.degree.name | Ph.D. | en_US |
| dc.identifier.bibrecord | .b34548610 | en_US |
| refterms.dateFOA | 2018-08-29T21:18:27Z | |
| html.description.abstract | In this dissertation, we identify a subgroup Tˢ of Dˢ(μ), the group of Sobolev symplectomorphisms of CP (n), n = 1,2 that has all the properties of a torus of a compact finite dimensional Lie group. We prove that Tˢ: (1) topologically is a submanifold of Dˢ(μ); (2) algebraically is a maximal abelian subgroup of Dˢ(μ); (3) geometrically is flat and totally geodesic. We also characterize the doubly stochastic operators on measurable spaces and use this result to extend the convexity Theorem of T. Bloch, H. Flaschka and T. Ratiu. |
