151-0530-00L Nonlinear Dynamics and Chaos II
|Semester||Spring Semester 2016|
|Periodicity||yearly recurring course|
|Language of instruction||English|
|Abstract||The internal structure of chaos; Hamiltonian dynamical systems; Normally hyperbolic invariant manifolds; Geometric singular perturbation theory; Finite-time dynamical systems|
|Objective||The course introduces the student to advanced, comtemporary concepts of nonlinear dynamical systems analysis.|
|Content||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
|Lecture notes||Students have to prepare their own lecture notes|
|Literature||Books will be recommended in class|
|Prerequisites / Notice||Nonlinear Dynamics I (151-0532-00) or equivalent|