Chaotic Dynamical Systems
5 credits
Syllabus, Master's level, 1MA260
A revised version of the syllabus is available.
- Code
- 1MA260
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 12 March 2009
- Responsible department
- Department of Mathematics
Entry requirements
120 credit points including Several Variable Calculus, Linear Algebra II and Ordinary Differential Equations I
Learning outcomes
In order to pass the course (grade 3) the student should be able to
- demonstrate a thorough knowledge of hyperbolicy, stable manifolds, homoclinic phenomena, structural stability, and symbolic dynamics;
- outline the construction of some ordinary strange attractors;
- carry out numerical studies of dynamical systems;
- outline some ordinary applications of the theory.
Content
Flows and Poincaré maps. Structural stability. Symbolic dynamics. Conjugation. Bifurcation theory. Stable and unstable manifolds. Homoclinic phenomena. Hyperbolicy. Chaos and sensitive dependence on initial data. Strange attractors. Numerical methods. Applications.
Instruction
Lectures and problem solving sessions.
Assessment
Oral and, possibly, written examination at the end of the course. Moreover, compulsory assignments may be given during the course.