INTRODUCTION TO DYNAMICAL SYSTEMS
Spring 2012

• Office : Padelford C-328
• Office Phone : (206) 685-1307
• E-mail : solomyak at math dot washington dot edu
• Office Hours : Mondays 3:30-4:30, Tuesdays 4:30-5:30, or by appointment

Course Information

• Text : S. Strogatz, Nonlinear Dynamics and Chaos, Westview, 1994, 2000.
• Lecture : MWF 1:30-2:20, ARC G070
• Homework (35% of overall grade) Weekly homework will be assigned.
• Midterm (25% of overall grade): Friday, May 4, in class.
• Final (40% of overall grade): Monday, June 4, 2:30-4:20.

• Syllabus

• Mathematica Notebook (iterated maps, adapted from Stan Wagon, Mathematica in Action, Freeman, 1991).

• In case this doesn't w-o-r-k on your computer, I also included a couple of p-r-o-g-r-a-m-s in a text file: Iteration in Mathematica

• Practice Final problems

• Practice problems: selected answers

Calendar and Homework Assignments

Turn in the problems in red.

Homework 1 (due W. April 4)     2.2.3, 4, 5, 8; 2.3.4; 2.4.2, 5.     Comments on Homework 1

Homework 2 (due W. April 11)     3.1.3, 3.2.4, 3.4.1, 3.4.5, 6, 8, 11.

Homework 3 (due W. April 18)     5.1.10, 5.1.11, 5.2.4, 5.2.10, 5.2.3, 5.2.5, 5.2.7, 5.2.9.

Homework 4 (due W. April 25)     6.1.5, 6.1.2, 6.1.6, 6.2.1, 6.3.2, 6.3.4, 6.3.6.

Homework 5 (due W. May 9)     6.5.2, 6.5.3, 6.6.1, 6.6.2, 6.8.2, 6.8.4, 7.2.14, 7.2.15.

Homework 6 (due W. May 16)     7.2.9, 7.2.10, 7.3.1, 7.3.10, 8.1.1, 8.1.6.

Homework 7 (due F. May 25)     10.1.1-10.1.8, 10.1.9, 10.1.11, 10.3.7, 10.3.8, 10.3.9.

Homework 8 (due F. June 1)     pdf file

5/25/2012:     More on logistic family, renormalization, and Lyapunov exponents.

5/23/2012:     Elements of symbolic dynamics, Sharkovskii's Theorem.

5/21/2012:     Conjugacy, tent-map and logistic map, chaos in the sense of Devaney.

5/18/2012:     Logistic map family (10.3 + other sources).

5/16/2012:     Exploring iteration with a computer.

5/14/2012:     Start iterated maps, cobwebs, linearization, stability of fixed points (10.1 + other sources).

5/11/2012:     Lorenz map (light coverage, Chapter 9)

5/9/2012:     Bifurcations revisited (light coverage, 8.1-8.2)

5/7/2012:     Limit cycles (cont.) (7.3-7.4)

5/4/2012:     Midterm;    Midterm solutions

5/2/2012:     Poincare-Bendixson Theorem (7.3)

4/30/2012:     Limit cycles (7.1-7.2)

4/27/2012:     Pendulum (6.7), Index theory (6.8)

4/25/2012:     Reversible systems (6.6)

4/23/2012:     Conservative systems (6.5)

4/20/2012:     Competing species (6.4)

4/18/2012:     Linearization (6.3)

4/16/2012:     Phase plane, existence and uniqueness for nonlinear 2D systems (6.1-2)

4/13/2012:     Love affairs (5.3) (student presentation)

4/11/2012:     Classification of linear systems, examples (5.2)

4/9/2012:     Linear systems, phase portraits, stability language (5.1-5.2)

4/6/2012:     Analysis of a population model: insect outbreak (3.7)

4/4/2012:     Pitchfork bifurcations (3.4), imperfect bifurcations and catastrophes (3.6)

4/2/2012:     Saddle-node and transcritical bifurcations (3.1 and 3.2)

3/30/2012:     Existence and uniqueness (2.5), start bifurcations (3.1)

3/28/2012:     Flows on the line (Sections 2.1-2.4)

3/26/2012:     Introduction (Chapter 1)