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151-0530-00L 4 Credits DR , MSC D-PHYS , D-MATH , D-MAVT
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Nonlinear Dynamics and Chaos II

Lecturers & Examiners: Prof. Dr. George Haller
VVZ CR n/a

Last Updated: 2026-02-05 15:41:53

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

Resources

Lecture Notes

Students have to prepare their own lecture notes

Literature

Books will be recommended in class

General Information

Language
English
Levels
DR , MSC
Frequency
Yearly recurring

Examination

Type
end-of-semester examination
oral examination

Course Components

Type Title Time & Place Hours
lecture with exercise Nonlinear Dynamics and Chaos II
  • Tue 16:15-18:00 (ML J 34.1)
  • Wed 10:15-12:00 (ML J 34.3)
4 h weekly

Offered In

  • Mechanical Engineering Master
    • Core Courses
      • Energy, Flows and Processes (The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.)
      • Mechanics, Materials, Structures (The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.)
      • Robotics, Systems and Control (The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor. .)
      • Micro & Nanosystems (The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.)
      • Bioengineering (The courses listed in this category “Core Courses” are recommended. Alternative courses can be chosen in agreement with the tutor.)
  • Computational Science and Engineering Master
    • Electives (In the ‘electives’ subcategory, at least two course units must be successfully completed.)
  • Mathematics Master
    • Application Area (Only necessary and eligible for the Master degree in Applied Mathematics. One of the application areas specified must be selected for the category Application Area for the Master degree in Applied Mathematics. At least 8 credits are required in the chosen application area.)
  • Physics Master
    • Electives
      • General Electives (Students may choose General Electives from the entire course programme of ETH Zurich - with the following restrictions: courses that belong to the first or second year of a Bachelor curriculum at ETH Zurich as well as courses from GESS "Science in Perspective" are not eligible here. The following courses are explicitly recommended to physics students by their lecturers. (Courses in this list may be assigned to the category "General Electives" directly in myStudies. For the category assignment of other eligible courses keep the choice "no category" and take contact with the Study Administration ( ) after having received the credits.))
  • Doctoral Department of Mathematics (More Information at: The list of courses (together with the allocated credit points) eligible for doctoral students is published each semester in the newsletter of the ZGSM. WARNING: Do not mistake ECTS credits for credit points for doctoral studies!)
  • Doctoral Department of Physics (More Information at: )