151-0530-00L  Nonlinear Dynamics and Chaos II

Semester Spring Semester 2014
Lecturers G. Haller
Periodicity two-yearly course
Course Does not take place this semester.
Language of instruction English



Catalogue data

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

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits 4 credits
Examiners G. Haller
Type session examination
Language of examination English
Course attendance confirmation required No
Repetition The performance assessment is only offered in the session after the course unit. Repetition only possible after re-enrolling.
Mode of examination written 60 minutes
Additional information on mode of examination The final grade will be based on 80 % homework and 20 % exam scores
Written aids written class notes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
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Courses

Number Title Hours Lecturers
151-0530-00 G Nonlinear Dynamics and Chaos II
Does not take place this semester.
3 hrs G. Haller

Restrictions

There are no additional restrictions for the registration.

Offered in

Programme Section Type
Doctoral Department of Mathematics Graduate School W Information
Doctoral Department of Physics Doctoral and Post-Doctoral Courses W Information
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Mechanical Engineering Master Micro- & Nanosystems and Processes W Information
Mechanical Engineering Master Medical Engineering W Information
Mathematics Master Control and Automation W Information
Mathematics Master Systems Design W Information