Suchergebnis: Katalogdaten im Frühjahrssemester 2023
Mathematik Master  | ||||||
 Wahlfächer (nur Fachrichtung Angewandte Mathematik MSc)Wahlfächer aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten, welche nur für das Master-Diplom in Angewandter Mathematik anrechenbar sind. | ||||||
| Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
|---|---|---|---|---|---|---|
| 151-0530-00L | Nonlinear Dynamics and Chaos II | W | 4 KP | 4G | G. Haller | |
| Kurzbeschreibung | The internal structure of chaos; Hamiltonian dynamical systems; Normally hyperbolic invariant manifolds; Geometric singular perturbation theory; Finite-time dynamical systems | |||||
| Lernziel | The course introduces the student to advanced, comtemporary concepts of nonlinear dynamical systems analysis. | |||||
| Inhalt | I. The internal structure of chaos: symbolic dynamics, Bernoulli shift map, sub-shifts of finite type; chaos is numerical iterations. II.Hamiltonian dynamical systems: conservation and recurrence, stability of fixed points, integrable systems, invariant tori, Liouville-Arnold-Jost Theorem, KAM theory. III. Normally hyperbolic invariant manifolds: Crash course on differentiable manifolds, existence, persistence, and smoothness, applications. IV. Geometric singular perturbation theory: slow manifolds and their stability, physical examples. V. Finite-time dynamical system; detecting Invariant manifolds and coherent structures in finite-time flows | |||||
| Skript | Handwritten instructor's notes and typed lecture notes will be downloadable from Moodle. | |||||
| Literatur | Books will be recommended in class | |||||
| Voraussetzungen / Besonderes | Nonlinear Dynamics I (151-0532-00) or equivalent | |||||
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