Analysis of low-dimensional dynamical systems; mainly maps of the circle, the annulus and the torus. Twist maps (existence of periodic points, versions of the invariant curve theorem, Aubry-Mather sets). Maps of the annulus or the torus with exotic behavior (examples by Furstenberg, Kan). Poincaré-Siegel theorem. Renormalization methods for period-doubling bifurcations and the Feigenbaum constant. Random products of matrices.
FSF3629 Constructions in Dynamical Systems 7.5 credits
This course has been discontinued.
Decision to discontinue this course:
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Information per course offering
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Course syllabus as PDF
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Course syllabus FSF3629 (Autumn 2016–)Headings with content from the Course syllabus FSF3629 (Autumn 2016–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
Intended learning outcomes
The students will learn several important techniques used in the theory of dynamical systems, including the KAM-methods, the method of approximations by conjugation, topological construction methods. The chosen techniques are central tools in the modern research of dynamical systems. In the course we give examples of application of these techniques to a variety of problems. This will give the students a broad overview of several active fields of research. The students will also practice and improve their presentation skills.
Literature and preparations
Specific prerequisites
A Master degree including at least 30 university credits (hp) in in Mathematics.
Knowledge of basic notions in dynamical systems and real analysis.
Literature
Several topics in the course are contained in the book “Introduction to the modern theory of dynamical systems” by A.Katok and B. Hasselblatt. Research articles can also be used.
Examination and completion
Grading scale
G
Examination
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
If the course is discontinued, students may request to be examined during the following two academic years.
Presentations of the course material and active participation at the lectures/seminars, or homework assignments and oral exam.
Other requirements for final grade
Satisfactory performance at presentations, or homework assignments completed and satisfactory oral test.
Examiner
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Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Education cycle
Third cycle