Dynamical Systems
10 credits
Syllabus, Master's level, 1MA217
A revised version of the syllabus is available.
- Code
- 1MA217
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N, 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, 9 April 2015
- Responsible department
- Department of Mathematics
Entry requirements
120 credits including 90 credits in mathematics with Real Analysis.
Learning outcomes
In order to pass the course (grade 3) the student should be able to
- calculate invariant manifolds and investigate their stability;
- calculate bifurcation diagrams for families of dynamical systems;
- account for hyperbolicity, invariant manifolds, homo- and heteroclinic phenomena and structural stability;
- analyse dynamical systems via symbolic dynamics;
- describe the structure of some common strange attractors.
Content
Flows and maps, invariant manifolds, linearisation, stability, phase portraits, Poincaré maps, structural stability, symbolic dynamics, horseshoes and invariant hyperbolic sets, Sharkovsky's theorem, conjugation, bifurcation theory, stable and unstable manifolds, homo- and heteroclinic phenomena, hyperbolicity, chaos and sensitive dependence on initial values, strange attractors.
Instruction
Lectures and problem solving sessions.
Assessment
Written examination at the end of the course combined with assignments.