INTRODUCTION TO DYNAMICAL SYSTEMS
Spring 2009

• Office : Padelford C-328
• Office Phone : (206) 685-1307
• E-mail : solomyak at math dot washington dot edu
• Office Hours : Mondays 1-2, Tuesdays 11-12, or by appointment

Course Information

• Text : K. Alligood, T. Sauer, J. Yorke. Chaos, An Introduction to Dynamical Systems, Springer 2000 (corrected edition).
• Lecture : MWF 10:30-11:20, MEB 246.
• Homework (35% of overall grade) Weekly homework will be assigned.
• Take-home exam (35% of overall grade): given May 27, due June 5.
• Project (30% of overall grade)

• Syllabus

• Homework 1 (due Wednesday, April 8); Selected solutions

• Homework 2 (due Friday, April 17); Handout on neutral fixed points and comments on the optional computing assignment

• Homework 3 (due Friday, April 24)

• Homework 4 (due Friday, May 1)

• Homework 5 (due Friday, May 8)

• Homework 6 (due Friday, May 15); Solution of T2.7 (extra credit)

• Homework 7 (due Friday, May 22)

• Homework 8 (due Wednesday, June 3)

Calendar/Announcements

5/18-20/2009:     Higher-dimensional differential equations (7.3, 7.4), start 7.5.

5/15/2009:     One-dimensional differential equations (7.1, 7.2)

5/11-13/2009:     Stable and unstable manifolds (2.6)

5/08/2009:     Two-dimensional maps (2.4, 2.5)

5/06/2009:     Two-dimensional maps (2.2, 2.3)

5/04/2009:     Box dimension (4.5, 4.6)

5/01/2009:     More on fractals. Computer demonstration. Mathematica Notebook

4/29/2009:     Iterated Function Systems, Chaos Game. IFS handout

4/27/2009:     Fractals from deterministic systems (4.3).

4/24/2009:     We skip 3.5 and begin 4.1 (Cantor set, fractals).

4/22/2009:     Sharkovski's Theorem (see Challenge 3 and Challenge 1).

4/20/2009:     Lyapunov exponents and chaotic orbits (Sections 3.1-3.2).

4/17/2009:     Chaos (after Devaney); more of Section 3.3.

4/15/2009:     Conjugacy (Section 3.3).

4/13/2009:     Sections 1.7-1.8 continued; doubling map; tent-map.

4/10/2009:     No Class today.

4/08/2009:     Sensitive dependence, itineraries (Sections 1.7-1.8).

4/06/2009:     Periodic Points (1.4), Logistic Map G(x)=4x(1-x) (Section 1.6).

4/03/2009:     Using Mathematica to study iteration. Logistic Family (Section 1.5). Hand-out (pdf) Hand-out (text)

Drawing the orbit diagram

4/01/2009:     Stability of fixed points (Section 1.3).

3/30/2009:     Introduction: what is this course about? Basic definitions in one-dimensional maps.