Chaotic Dynamical Systems
Syllabus, Master's level, 1MA046
This course has been discontinued.
- Code
- 1MA046
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N
- Grading system
- Pass with distinction (5), Pass with credit (4), Pass (3), Fail (U)
- Finalised by
- The Faculty Board of Science and Technology, 15 March 2007
- Responsible department
- Department of Mathematics
Entry requirements
BSc, Several Variable Calculus, Linear Algebra II, Ordinary Differential Equations I
Learning outcomes
In order to pass the course (grade 3) the student should be able to
Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.
Content
Existence and uniqueness theorems for solutions of ordinary differential equations, numerical methods, flows, parameter and initial value dependence, fix points, periodic orbits, limit cycles, linearisation, stability and Lyapunov functions, phase portraits, Poincaré–Bendixson's theorem, Grönwall's lemma, Poincaré maps. Structural stability, symbolic dynamics, conjugation, bifurcation theory, stable and unstable manifolds, homoclinic phenomena, hyperbolicy, chaos and sensitive dependence on initial data, strange attractors. Applications.
Instruction
Lectures and problem solving sessions.
Assessment
Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.