Chaotic Dynamical Systems

Course manual 2020/2021

Course content

Modern dynamical systems theory originates with the work of Poincare, who revolutionized the study of dynamical systems by introducing qualitative techniques of geometry and topology to discuss global properties of solutions. The study of chaotic dynamical systems from the 1960s on lead to a breakthrough in science and an explosion of interest in the field of dynamical systems.

This course investigates nonlinear dynamical systems and explains basic ideas of the field in low dimensional settings of iterated maps on the line and in the plane. Important results and ideas are explained in this context, such as symbolic dynamics, "period three implies chaos" and the Shaskovskii theorem, period doubling route to chaos and dynamics of torus maps.

Study materials

Literature

• G.R. Goodson. Chaotic Dynamics. Fractals, Tilings, and Substitutions.

Objectives

• The student can explain mechanisms causing chaos in interval maps.
• The student is able to apply techniques to investigate chaotic maps.

Teaching methods

• Zelfstandig werken aan bijv. project/scriptie
• Presentatie/symposium
• Hoorcollege
• Werkcollege
• Lecture
• Self-study
• Exercise class
• Working independently on e.g. a project or thesis

Learning activities

Attendance

Programme's requirements concerning attendance (OER-B):

• Each student is expected to actively participate in the course for which he/she is registered.
• If a student can not be present due to personal circumstances with a compulsory part of the programme, he / she must report this as quickly as possible in writing to the relevant lecturer and study advisor.
• It is not allowed to miss obligatory parts of the programme's component if there is no case of circumstances beyond one's control.
• In case of participating qualitatively or quantitatively insufficiently, the examiner can expel a student from further participation in the programme's component or a part of that component. Conditions for sufficient participation are stated in advance in the course manual and on Canvas.
• In the first and second year, a student should be present in at least 80% of the seminars and tutor groups. Moreover, participation to midterm tests and obligatory homework is required. If the student does not comply with these obligations, the student is expelled from the resit of this course. In case of personal circumstances, as described in OER-A Article A-6.4, an other arrangement will be proposed in consultation with the study advisor.

Additional requirements for this course:

 Grades for homework and the group project do not count for the resit. Participation in the group project is required for taking the resit.

Assessment

 Calculators and literature are not allowed for the tests

Assignments

Group project

• Takes place in small groups. Graded by report and presentation

Homework exercises

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Timetable

The schedule for this course is published on DataNose.

Honours information

There is no honours extension of this course.

Contact information

Coordinator

• prof. dr. Ale Jan Homburg