Geometry and dynamics
Ects : 6
Enseignant responsable :
Volume horaire : 39Description 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.
Compétence à acquérir :
Introduction to manifolds and the geometric viewpoint of dynamical systems.