Introduction to dynamical systems
Summary
An introduction to some key concepts and theorems from dynamical systems, including discrete dynamical systems as well as flows.
Content
-abstract dynamical systems
-ergodicity
-Poincare recurrence
-Birkhoff theorem
-invariant manifolds and hyperbolicity
-Conjugation problem
-Poincare-Bendixson theory.
Learning Prerequisites
Required courses
Analysis I - IV, Algebre Lineaire I and II.
Recommended courses
Analysis I - IV, Algebre Lineaire I and II.
Important concepts to start the course
Understand key concepts of real analysis, such as measure and Lebesgue integral. Some familiarity with Fourier series and ordinary differential equations. Be able to construct a rigorous mathematical argument.
Learning Outcomes
By the end of the course, the student must be able to:
- Analyze abstract dynamical systems
- Examine issues concerning the local and global behavior of dynamical systems
- Prove basic results, such as Poincare recurrence.
- Contrast different dynamical behaviors.
Assessment methods
Oral exam
Supervision
| Office hours | No |
| Assistants | Yes |
| Forum | No |
Dans les plans d'études
- Semestre: Automne
- Forme de l'examen: Oral (session d'hiver)
- Matière examinée: Introduction to dynamical systems
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Oral (session d'hiver)
- Matière examinée: Introduction to dynamical systems
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Oral (session d'hiver)
- Matière examinée: Introduction to dynamical systems
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Oral (session d'hiver)
- Matière examinée: Introduction to dynamical systems
- Cours: 2 Heure(s) hebdo x 14 semaines
- Exercices: 2 Heure(s) hebdo x 14 semaines
- Type: optionnel