151-0530-00L  Nonlinear Dynamics and Chaos II

SemesterSpring Semester 2021
LecturersG. Haller
Periodicityyearly recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
151-0530-00 GNonlinear Dynamics and Chaos II4 hrs
Tue16-18ML J 34.1 »
Wed10-12ML 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
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
RepetitionA repetition date will be offered in the first two weeks of the semester immediately consecutive.
Additional information on mode of examinationoral examination

Learning materials

 
Additional linksNonlinear Dynamics and Chaos I. / Moodle course
Only public learning materials are listed.

Groups

No information on groups available.

Restrictions

There are no additional restrictions for the registration.

Offered in

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Doctoral Department of MathematicsGraduate SchoolWInformation
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Mechanical Engineering MasterEnergy, Flows and ProcessesWInformation
Mechanical Engineering MasterMechanics, Materials, StructuresWInformation
Mechanical Engineering MasterRobotics, Systems and ControlWInformation
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Mechanical Engineering MasterBioengineeringWInformation
Mathematics MasterControl and AutomationWInformation
Mathematics MasterSystems DesignWInformation
Physics MasterGeneral ElectivesWInformation
Computational Science and Engineering MasterElectivesWInformation