Credits: 9

Type: advanced and professional

Objectives:

To study the global properties of solutions to differential equations and the orbits for diffeomorphisms using analytical, geometric and topological techniques.

Knowledge:

• Continuous and discrete dynamical systems.
• Local structure.
• Normal forms and bifurcations.
• Hyperbolicity.
• Introduction to chaotic dynamical systems.

Subject-specific competences:

• To be able to analyse the behaviour of a system around a fixed point.
• To show knowledge of a family of dynamical systems and the characteristic features of its phases and analysis of bifurcations.
• To show understanding of hyperbolicity and its consequences.
• To show an understanding of the conditions in which symbolic dynamics can be used in continuous systems and the effects of this use.