This course will lay the mathematical foundations for analyzing the dynamical systems that appear in engineering and science. The mathematical techniques will be brought to bear on problems from physics and chemistry.

• Determine when there are existence and uniqueness of solutions to a system of ordinary differential equations.
• Prove and disprove stability of a solution using Hartman-Grobman theorem and Lyapunov exponents.
• Operate with dynamically defined, invariant manifolds.
• Apply Poincaré-Bendixon theorem to show the existence of limit cycles.
• Apply Index theory in the plane as well as compactification to rule out certain dynamical descriptions.
• Classify local bifurcations in general and find the possible local bifurcations in a specific system.
• Simulate a dynamical system
• Combine the aforementioned points to give a global description of certain dynamical systems.

Existence and uniqueness of solutions to systems of ordinary differential equations. Attracting, repelling and neutral manifolds. Stability analysis including the Hartman-Grobman theorem and Lyapunov exponents. Theory of planar systems including Poincaré-Bendixon theorem and index theory. Local bifurcation theory.

Please contact the teacher for information on whether this course gives the student the opportunity to prepare a project that may participate in DTU´s Study Conference on sustainability, climate technology, and the environment (GRØN DYST). More information http://www.groendyst.dtu.dk/kursustilmelding.aspx