151-0530-00L  Nonlinear Dynamics and Chaos II

SemesterSpring Semester 2023
LecturersG. Haller
Periodicityyearly recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
151-0530-00 GNonlinear Dynamics and Chaos II4 hrs
Tue16:15-18:00ML J 34.1 »
Wed10:15-12:00ML J 34.3 »
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 notesHandwritten instructor's notes and typed lecture notes will be downloadable from Moodle.
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.
Mode of examinationoral 30 minutes

Learning materials

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Only public learning materials are listed.

Groups

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Restrictions

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Offered in

ProgrammeSectionType
Doctorate PhysicsSubject SpecialisationWInformation
Mechanical Engineering MasterEnergy, Flows and ProcessesWInformation
Mechanical Engineering MasterMechanics, Materials, StructuresWInformation
Mechanical Engineering MasterRobotics, Systems and ControlWInformation
Mechanical Engineering MasterMicro & NanosystemsWInformation
Mechanical Engineering MasterBioengineeringWInformation
Mathematics MasterElectives (Direction Applied Mathematics MSc Only)WInformation
Mathematics MasterControl and AutomationWInformation
Mathematics MasterSystems DesignWInformation
Physics MasterGeneral ElectivesWInformation
Computational Science and Engineering MasterElectivesWInformation