Complexe de Morse et bifurcations
dc.contributor.advisor | Cornea, Octavian | |
dc.contributor.author | Duquerroix, Florian | |
dc.date.accessioned | 2015-05-25T15:38:33Z | |
dc.date.available | NO_RESTRICTION | fr |
dc.date.available | 2015-05-25T15:38:33Z | |
dc.date.issued | 2015-04-30 | |
dc.date.submitted | 2015-01 | |
dc.identifier.uri | http://hdl.handle.net/1866/11970 | |
dc.subject | Théorie de Morse | fr |
dc.subject | Homotopie | fr |
dc.subject | Bifurcation | fr |
dc.subject | Singularité | fr |
dc.subject | Naissance | fr |
dc.subject | Mort | fr |
dc.subject | Glissement d'Anse | fr |
dc.subject | Morse Theory | fr |
dc.subject | Continuation | fr |
dc.subject | Singularity | fr |
dc.subject | Birth | fr |
dc.subject | Death | fr |
dc.subject | Handle-Slide | fr |
dc.subject.other | Mathematics / Mathématiques (UMI : 0405) | fr |
dc.title | Complexe de Morse et bifurcations | fr |
dc.type | Thèse ou mémoire / Thesis or Dissertation | |
etd.degree.discipline | Mathématiques | fr |
etd.degree.grantor | Université de Montréal | fr |
etd.degree.level | Maîtrise / Master's | fr |
etd.degree.name | M. Sc. | fr |
dcterms.abstract | Soit une famille de couples (ft,Xt)t∈J , où J est un intervalle, ft est une fonction lisse à valeurs réelles définie sur une variété lisse et compacte V , et Xt est un pseudo-gradient associé à la fonction ft. L’objet de ce mémoire est l’étude des bifurcations subies par les complexes de Morse associés à ces couples. Deux approches sont utilisées : l’étude directe des bifurcations et l’approche par homotopie. On montre que finalement ces deux approches permettent d’obtenir les mêmes résultats d’un point de vue fonctoriel. | fr |
dcterms.abstract | Let (ft,Xt)t∈J be a family of pairs, where J is an interval, ft is a smooth real-valued Morse function defined on a smooth compact manifold V , and Xt is a pseudo-gradient field associated to ft. The purpose of this master thesis is to study the bifurcations undergone by the associated Morse complexes. Two ways are used to reach this result : the direct study of the bifurcations and the continuation method. We prove that the two methods produce the same results from a functorial point of view. | fr |
dcterms.language | fra | fr |
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