Spring 2023, Stonybrook, Undergraduate Level. 

Class Meetings: Tuesday and Thursday 1:15 pm - 2:35 pm, Physics P113

Instructor: Donghao Wang

Email: donghao.wang233333@stonybrook.edu (remove all numbers)

Office Hours:  Wednesday 4: 00 pm - 6: 00 pm at SCGP Room 310

                                 Wednesday 6: 00 pm - 7: 00 pm online via zoom.       

                                        also            by appointments

Textbook:  Chaos: An Introduction to Dynamic Systems, by Alligood, Sauer, and Yorke.

                         This book can be downloaded here and is referred to as ASY below. We will try to cover most of Chapter 1 - 8. 

Course syllabus can be found here.

Other Useful Sources: An introduction to Chaotic Dynamic Systems, by Devaney.

                                                  A First Course in Dynamics with panorama of recent developments, by Hasselblatt and Katok

                                                  Differential Equations, Dynamical Systems, and an Introduction to Chaos, by Devaney, Hirsch, and Smale.

                                                  Dynamics in One Complex Variable, by Minor.

                                                 Complex Analysis: The Argument Principle in Analysis and Topology, by Beardon

Schedule and Suggested Readings (will be updated as it goes): 

1. Tu 1/24 (Notes) ASY 1.1: Introduction

2. Th 1/26 (Notes) ASY 1.2-1.4: Stability of Fixed Points and Periodic Points 

3. Tu 1/31 (Notes) ASY 1.4-1.5: Families of Logistic Maps. 

4. Th 2/2 (Notes) ASY 1.6-1.8: Sensitive Dependence on Initial Conditions. 

5. Tu 2/7 (Notes) ASY 1.8: More examples on Sensitive  Dependence. 

6. Th 2/9 (Notes) ASY 2.1 & 2.3: Simple Linear Systems in Dimension 2 (HW1 DUE)(Solutions)

7. Tu 2/14 (Notes) ASY 2.2 & 2.4: Linear Systems, Stability and Change of Coordinate. 

8. Th 2.16 (Notes) ASY 2.5: Non-linear Maps. 

9. Tu 2/21 (Notes) ASY 2.6: A Digression on Bifurcation and the Stable Manifold Theorem. 

10. Th 2/23 (Notes) ASY 3.1-3.2: Lyapunov numbers and Chaotic orbits. (HW2 DUE)(Solutions)

11. Tu 2/28 (Notes) ASY 3.3: Conjugacy.

12. Th 3/2  (Notes) ASY 3.4: Three implies all periods. 

13. Tu 3/7 (Notes) ASY 4.1 & 4.3: The 1/3-Cantor Set.

14. Th 3/9 (Notes) ASY 4.2 - 4.4 : More examples on Fractals (HW3 DUE)

** Tu 3/14 (Spring Break!)

** Th 3/16 (Spring Break!)

15. Tu 3/21: Midterm (Solution)

16. Th 3/23: (Notes) ASY 4.5-4.6: Fractal Dimension. 

17. Tu 3/28: (Notes) ASY 2.7 & 5.1: Lyapunov numbers in higher dimensions. 

18. Th 3/29 (Rescheduled from 3/30) (Notes): ASY 5.4: Fixed Points Theorem (We will skip Section 5.2 & 5.3)

19. Tu 4/4: (Notes) ASY 5.4: Fixed Points Theorem Continued.

20. Th 4/6: (Notes) ASY 5.5 & 5.6: Markov Partition (HW4 DUE)

21. Tu 4/11: (Notes) ASY 6.1-6.2: Chaotic Attractors and Examples

22. Th  4/13: (Notes) ASY 6.3-6.4: More Examples: Piecewise Linearly Expanding Maps.

23. Tu 4/18: (Notes) ASY 6.5-6.6: Natural Measures.

24. Th 4/20: (Notes) ASY 7.1-7.2: 1-Dimensional ODE (HW5 DUE)

25. Tu 4/25: (Notes) ASY 7.3: 2-Dimensional Linear ODE

26. Th 4/27: (Notes) ASY 7.4-7.5: Non-linear 1st Order ODE in general

27. Tu 5/2: (Notes) ASY 7.5-7.6: Lyapunov Functions and Stability

28. Th 5/4: (Notes) ASY 8.1 (HW6 DUE)(HW7 Optional)

** Final: Mon 5/15 11:15 am to 1:45 pm