UE5 Dynamical Systems S9 SM2NLP

Objectives: Introduction to the basic notion of the theory of dynamical systems.

Organization: CM: 15 h, TD: 10 h.

Necessary background: general knowledge of physics

Topics of the course: Autonomous differential equations, fixed points and periodic orbits, Poincare-Bendixon theorem, theory of bifurcations. Linearization, Lyapunov exponents, stable and unstable manifolds. Hamiltonian systems, phase space, invariant tori, action-angle variables, problem of small denominators, the KAM theorem, application to the motion of asteroids. Dissipative systems, chaos, attractors, fractal dimensions.

Skills to be achieved:
Understanding the basic principles of the dynamical system approach.
Ability to qualitatively analyze a simple dynamical system.

Grading plan:
Session 1: Written exam (ET) : 100%
Session 2: Written exam (ET) : 100%