Course Syllabus for

Non-linear Dynamical Systems
Olinjära dynamiska system

FMAN15F, 7.5 credits

Valid from: Autumn 2014
Decided by: FN1/Anders Gustafsson
Date of establishment: 2015-03-15

General Information

Division: Mathematics
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: FMAN15
Teaching language: English


To give knowledge of and familiarity with concepts and methods from the theory of dynamical systems which are important in applications within almost all subjects in science and technology.


Knowledge and Understanding

For a passing grade the doctoral student must

Competences and Skills

For a passing grade the doctoral student must

Course Contents

Dynamical systems in discrete and continuous time. The fixed point theorem and Picard's theorem on the existence and uniqueness of solutions to ordinary differential equations. Phase space analysis and Poincaré's geometrical methods. Local stability theory (Liapunov's method and Hartman-Grobman's theorem). The central manifold theorem. Basic local bifurcation theory. Global bifurcations and transition to chaos. Chaotic and strange attractors (dynamics, combinatorial description).

Course Literature

Instruction Details

Types of instruction: Lectures, exercises

Examination Details

Examination formats: Written exam, oral exam, written assignments. Written and/or oral test, to be decided by the examiner. Some written assignments to be completed before the exam.
Grading scale: Failed, pass

Admission Details

Assumed prior knowledge: FMAF05 Systems and Transforms, or similar

Course Occasion Information

Contact and Other Information

Course coordinators:
Web page:

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