[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-957881","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n  \u003Cdiv class=\u0022row\u0022\u003E\n    \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n      \u003Ch2 class=\u0022h1 text-left\u0022\u003E  M\u00e9thodes analytiques en dynamique hyperbolique 2025-2026\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          6\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemestre calendaire :\n          Semester 2\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ECours magistraux :\u003C\/span\u003E\n                                      \u003Cspan\u003E20\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                                                                        \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EAnglais\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003Enon\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n    \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EPr\u00e9requis\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EIl pourra \u00eatre utile (bien que non n\u00e9cessaire) d\u2019avoir suivi les cours suivants du M2 AAG au premier semestre : - Introduction aux syst\u00e8mes dynamiques topologiques et di\ufb00\u00e9rentiables - Introduction \u00e0 l\u2019analyse semiclassique Des rappels d\u2019analyse et de dynamique seront toutefois faits au d\u00e9but du cours.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003ER\u00e9sum\u00e9 : Le but de ce cours est l\u2019\u00e9tude des propri\u00e9t\u00e9s statistiques (ergodicit\u00e9, m\u00e9lange, m\u00e9lange exponentiel, etc.) des syst\u00e8mes dynamiques uniform\u00e9ment hyperboliques tels que les di\ufb00\u00e9omorphismes d\u2019Anosov, ou le flot g\u00e9od\u00e9sique sur les surfaces \u00e0 courbure n\u00e9gative. Nous adopterons un point de vue moderne fond\u00e9 sur l\u2019analyse microlocale, c\u2019est-\u00e0-dire l\u2019\u00e9tude des singularit\u00e9s des solutions des \u00e9quations aux d\u00e9riv\u00e9es partielles lin\u00e9aires. Notions \u00e9tudi\u00e9es : - Rappels d\u2019analyse, calcul pseudodi\ufb00\u00e9rentiel - Rappels de dynamique hyperbolique : d\u00e9finitions, exemples, propri\u00e9t\u00e9s \u00e9l\u00e9mentaires - Op\u00e9rateur de transfert, distributions anisotropes - M\u00e9lange exponentiel des di\ufb00\u00e9omorphismes d\u2019Anosov - Fonctions zeta, d\u00e9terminants dynamiques\u003C\/p\u003E\n\u003Cp\u003ESummary: The goal of this course is to study the statistical properties (ergodicity, mixing, exponential mixing, etc.) of uniformly hyperbolic dynamical systems such as Anosov di\ufb00eomorphisms or the geodesic flow on negatively curved surfaces. We will adopt a modern viewpoint based on microlocal analysis, that is, the study of the singularities of solutions to linear partial di\ufb00erential equations. Topics covered: - Review of analysis, pseudodi\ufb00erential calculus - Review of hyperbolic dynamics: definitions, examples, basic properties - Transfer operator, anisotropic distributions - Exponential mixing of Anosov di\ufb00eomorphisms - Zeta functions, dynamical determinants\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                                        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EBibliographie\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EThibault Lefeuvre, Microlocal analysis in hyperbolic dynamics and geometry, Cours sp\u00e9cialis\u00e9s de la SMF, 2025. https:\/\/thibaultlefeuvre.blog\/microlocal-analysis-in-hyperbolic-dynamics-and-geometry-2\/\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EEvaluation Terminale\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]