Humiliere, Vincent (2008) Continuity in symplectic topology. PhD thesis CMAT, CMAT, EP/X p.154.
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Alternative Locations: http://www.imprimerie.polytechnique.fr/Theses/Files/Humiliere.pdf
Abstract
In this thesis, we study several problems from symplectic topology, where C°-topology interfere.
We study some completions of the space of Hamiltonian maps, and apply this study to the Hamilton-Jacobi equations. Then, we tackle the problem of the extension of the Calabi morphism to some homeomorphism groups. Finally, we consider the C°-rigidity of Poisson bracket and the extension to the continuous framework of the notion of Hamiltonian representation.
| Item Type: | PhD Thesis (PhD) |
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| PhD Supervisor: | Viterbo, Claude |
| Date: | 09 July 2008 |
| Board of examiners: | Patrick, Bernard and Paul, Biran and Frédéric, Bourgeois and Emmanuel, Giroux and Patrice, Le Calvez |
| Ecole Doctorale: | ED 447 ECOLE DOCTORALE DE L'ECOLE POLYTECHNIQUE |
| Discipline: | CMAT |
| Collection (Fonds): | Ecole Polytechnique (EP/X) |
| Institution: | EP/X |
| Department: | CMAT |
| Subjects: | 1. Mathematics and Applications |
| Uncontrolled Keywords: | Symplectic topology, Hamiltonian dynamics, Hamilton-Jacobi equations, Poisson brackets, Calabi invariant, Topologie symplectique, Dynamique hamiltonienne, Equation d'Hamilton-Jacobi, Crochet de Poisson, invariant de Calabi |
| ID Code: | 4108 |
| Deposited By: | Laurence Vidament |
| Deposited On: | 29 August 2008 |
Table of content
Introduction
Chap 1. Des distances remarquables
Chap 2. Extension de la dynamique hamiltonienne
Chap 3. Equations dHamilton-Jacobi dévolution
Chap 4. Haméomorphismes
Chap 5. Pseudo-représentations et rigidité du crochet de Poisson
Annexe A. Outils
Annexe B. Fonctions génératrices
Annexe C. Valeurs critiques de "min-max"
Annexe D. Une preuve de la non-dégénérescence de la distance de Hofer
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