Nichtlineare Dynamik: Grundlagen

What it is about

You will learn the fundamentals of the theory of finite-dimensional continuous and discrete dynamical systems: phase space analysis, stability, bifurcations and initial insights into chaotic dynamics. In the end you will be able to apply these concepts to concrete examples and apply the most important analytical methods.

What you will be able to do

• Understanding the mathematical theory of finite-dimensional dynamical systems
• Mastery of phase space analysis ( equilibria, periodic orbits, invariants, stability )
• Applying linearization and Poincaré-Bendixson theory
• Recognizing and analyzing steady-state bifurcations (fold, Hopf)
• Basic knowledge in perturbation theory, asymptotics and multi-scale methods
• Classifying simple chaotic examples (one-dimensional maps, 3D flows) and fundamentals of symbolic dynamics

What the module consists of

• VorlesungPresentation and derivation of the relevant mathematical concepts and proofs; serves as motivation for independent deepening
• ÜbungenIndependent work on problem sheets for preparation and deepening; applications of the lecture content to examples

Teaching method

• TafelvortragConcepts and methods are derived and proven in detail
• Aufgabenblätter / HausaufgabenPromote independent engagement and practice applying the methods to concrete problems