151-0530-00L  Nonlinear Dynamics and Chaos II

SemesterSpring Semester 2018
LecturersG. Haller
Periodicityyearly recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
151-0530-00 GNonlinear Dynamics and Chaos II4 hrs
Wed10:15-12:00HG F 26.3 »
Thu16:15-18:00ML J 34.3 »
29.03.16:15-17:00ML J 34.3 »
14.05.10:15-12:00ML H 37.1 »
15.05.16:15-18:00HG F 26.5 »
G. Haller

Catalogue data

AbstractThe internal structure of chaos; Hamiltonian dynamical systems; Normally hyperbolic invariant manifolds; Geometric singular perturbation theory; Finite-time dynamical systems
Learning objectiveThe course introduces the student to advanced, comtemporary concepts of nonlinear dynamical systems analysis.
ContentI. 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 notesStudents have to prepare their own lecture notes
LiteratureBooks will be recommended in class
Prerequisites / NoticeNonlinear 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 credits4 credits
ExaminersG. Haller
Typeend-of-semester examination
Language of examinationEnglish
RepetitionThe performance assessment is only offered at the end after the course unit. Repetition only possible after re-enrolling.
Additional information on mode of examinationoral examination

Learning materials

 
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Mathematics MasterControl and AutomationWInformation
Mathematics MasterSystems DesignWInformation
Physics MasterGeneral ElectivesWInformation