Department of Mathematics, KTH

Group in dynamical systems and number theory.

SF2720, Chaotic Dynamical Systems, Fall 2012

This is an introductory course to Dynamical Systems.

Topics include:

  • One-dimensional dynamics, including circle homeomorphisms and quadratic maps

  • Coding and symbolic dynamics, recurrence, chaos

  • Hyperbolic dynamics: hyperbolic sets, invariant manifolds.

  • Poincaré-Bendixson theorem





A written final exam (only pencil and rubber) will be given on Monday January 28, from 9:00—13:00 (4 hours) in room D32.

If you plan to write the exam, please contact Maria or Kristian (if you have not already done so).







Reading instructions and homework assignments: Here you will find recommendations of what to focus on in the course book (see below).

  1. The first two lectures have essentially covered material from Ch. 1, ch. 2.1-2.3 (only the case of one variable; interval maps and circle maps) , ch. 2.5, ch. 11.1 and ch. 11.3.2-11.3.3. This material should be enough to solve the first homework assignment.

Here you find Homework assignment 1. They are due Sept. 28. (In problem 4 you should assume that the functions f and g are both continuously differentiable, as it now says in the problem formulation.)

    2. During the third lecture we started looking at rotations of the circle. We covered (parts of) ch. 4.1.1 - 4.1.4 (and 2.6.2 about the circle).

    Here you find Homework assignment 2. The exercises are due October 26.

    Here you find Homework assignment 3. The exercises are due November 23.

    Here you find Homework assignment 4. The exercises are due December 14.



Time and place: Fridays 10:15 – 12:00 in room 3733 at the Department of Mathematics, KTH.

Course starts: Friday September 7.

Instructors: Kristian Bjerklöv (bjerklov at kth dot se) & Maria Saprykina (masha at kth dot se)

Examination: Homework problems (to get grade E or Pass) and a final exam (a written exam for those having grade E, aiming at a higher grade).

Textbook: A first course in dynamics, with a panorama of recent developments, by Boris Hasselblatt and Anatole Katok.

You can find information about the book and an errata here.




About Dynamical systems from Wikipedia.