Till matematikens huvudsida | Tillbaka till kurssidorna

Matematiska Institutionen

Kursernas Hemsidor

273027 Introduction to Dynamical Systems 2012 (5 sp)

The course treats fundamental notions in the theory of discrete-time dynamical systems, such as periodicity, attraction/repulsion, bifurcations, chaos and sensitive dependence on initial conditions ("the butterfly effect"). In the multidimensional case we give a survey of classical stability theory for linear systems.

The course in given, in English or Swedish depending on the audience, by professor Göran Högnäs on Mondays 10-12 in aud. Vectorrummet, Tuesdays 13-15 and Fridays 13-15 in aud. Hilbertrummet B329 on the 3rd floor of the ASA building.

The course starts on Monday, January 9 at 1 p.m. and ends on Friday, March 9. There are weekly exercise sessions, but in addition some larger individual project work will also be assigned. The examination is a 24-hour open-book examination. Preliminary examination date is Thursday-Friday, March 8-9.
Course outline.

Prerequisites: Calculus and some course in linear algebra (matrices) and differential equation.

Course material: R. L. Devaney: An Introduction to Chaotic Dynamical Systems, Addison-Wesley, 2nd ed. 1989 (or later editions). Additional handouts will be distributed.

The handouts can now be downloaded as pdf-files below:
A1-10 contains preliminary material from Calculus needed in the course.

Lecture notes:

• 1-12.
• 13-18.
• 19-27.
• 28-35.
• 36-45.
• 46-53.
• 54.
• 55-50.
• 61-68.
• 68-75.
• 81.
• 76-86.
• 87-92.
• 93-99.

• Friday, January 20 dyn1.pdf.
• Friday, January 27 dyn2.pdf.
• Friday, February 3 dyn3.pdf.
• Friday, February 10 dyn4.pdf.
• Friday, February 17 dyn5.pdf.
• Friday, February 24 dyn6.pdf.
• Friday, March 2 dyn7.pdf.

Hemarbete B 28 februari.

CentralaBegrepp important notions.

Pictures of periods

On Intervals, Transitivity = Chaos by Vellekoop and Berglund

Terminology and exercises. Some exercises from the book.

More course material:

Teaching material from 2009