| Crédit : 6 ECTS |
| Langue du cours : anglais
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Volume horaire
- CM :
39 h
- Volume horaire global (hors stage) :
39 h
Compétences à acquérir
Introduction to manifolds and the geometric viewpoint of dynamical systems.
Description du contenu de l'enseignement
This course provides an introduction to manifolds and to the geometric viewpoint on dynamical systems and differential equations.
- Reminders of differential calculus, local inversion
- Manifolds : local coordinates, examples (parametrization, equation : sphere, torus), tangent vectors and space, maps, derivative
- Differential equations (flow, phase portrait in dimension 2, conjugacy). Examples: linear differential equations in the plane, gradient flows and optimization problems, geodesic flows and mechanical problems
- Equilibria of autonomous equations and their stability, periodic orbits and Poincaré maps.
Enseignant responsable
ANNA FLORIO