Modul

The module will be completed with an oral exam of about 30 minutes.

After successful completion of this module students

• can explain the significance of dynamical systems and give several examples;
• have acquired miscellaneous tools to prove the existence of special solutions and to analyze the local dynamics around them;
• master several techniques to describe global dynamics in certain classes of dynamical systems;
• identify various bifurcations and explain how these change the dynamics of the system;
• outline the main steps in establishing chaotic behavior.

None

• Flows
• Abstract dynamical systems
• Lyapunov functions
• Invariant sets
• Limit sets and attractors
• Hartman-Grobman theorem
• Local (un)stable manifold theorem
• Poincaré-Bendixson theorem
• Periodic orbits and Floquet theory
• Exponential dichotomies
• Melnikov functions
• Lin's method
• Hamiltonian dynamics
• Liénard systems
• Bifurcations
• Chaotic dynamics
• (Introduction to) Fenichel theory
• Center manifolds
• Dynamical systems associated with semilinear evolution equations

The following modules are strongly recommended: Analysis 1-2 and Linear Algebra 1-2. The module Analysis 4 is recommended.

Total workload: 180 hours

Attendance: 60 h

•  lectures, problem classes and examination

Self studies: 120 h

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research on the course content,
• preparation for the module examination