151-0530-00L  Nonlinear Dynamics and Chaos II

Semester Frühjahrssemester 2016
Dozierende G. Haller
Periodizität jährlich wiederkehrende Veranstaltung
Lehrsprache Englisch

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 Students have to prepare their own lecture notes
Literatur Books will be recommended in class
Voraussetzungen / Besonderes Nonlinear Dynamics I (151-0532-00) or equivalent