Relating to the MAT551 course and under the supervision of the professor, students prepare a personal work leading to a thesis and a defense.
These in-depth courses are the opportunity to complete and enhance the MAT551 course "Dynamical Systems". Subjects are chosen after discussion and will to a short introductory course. Here are some subjects proposed or addressed from last years:
- Hyperbolic set stability and examples of sturdily unstable systems
- Homoclinic orbit and chaotic behabior in classic mechanics
- Furstenberg theory: ergodic proof of the combinatory Sremerédi theorem
- KAM theorem and Arnold diffusion: stability and unstability in hamiltonian systems
- Group acting on the circle
- Count geodetics
- Jewett-Krieger realisation theorem
- The Pugh closing lemma
- The Hopf argument
All the proposals with an important mathematics part, particularly in connection with other courses (e.g. control theory, probabilities, mechanics, ...), are welcomed.
The course structure is flexible, personal work on documents playing a key role. Evaluation will be a detailed thesis and a defense to show that you have a synthetic mind and can answer specific questions.
Course language: French
- Profesor: Burguet David