# Math 307, Dynamical Systems & Chaos, Fall 2011

### Instructor

Marius Ionescu
Office: 201K MCGREG
email: mionescu at colgate.edu
Office Hours:Tu 12:30-2:00; We 2:30-4:00

### Classes

• TTh 2:45-4:00pm 204 MCGREG

### Homework

The homework assignments are due on Thursdays at the beginning of the class

### Lectures

1. Lectures 1, 2, and 3: 08/30/11, 09/01/2011, 09/06/2011 Chapter 1: One dimensional maps; coweb plots; fixed and periodic points; fixed point theorems; periodic orbits; family of logistic maps.
Some Matlab programs:
Iterating the logistic map, Drawing a cobweb diagram, with the logistic function, Finding the fixed points of a logistic map, finding the fixed points of the second iterate of a logistic map, Finding the zeros for the logistic map and second iterate Bifurcation diagram (from Wikipedia)

2. Homework #1, due Thursday, September 15: Text exercises: TI.4 (this problem has the answer to the first part in the bak of the book), TI.6,TI.13; Exercises: (page 36) 1.3, 1.7, 1.8.; Computer projects: (you can work in groups for these projects; feel free to use my codes if you need them)
• Computer experiment 1.2;
• write a code that plots the bifurcation diagram (Figure 1.6 on page 19)
3. Lecture 4, 09/08/11 Sections 1.6, 1.7;
4. Lectures 5 and 6, 09/13 and 09/15 Sections 1.8, 2.2,2.3,2.4; Please review the Matrix Algebra appendix; Henon map program

5. Homework #2, due Thursday, September 29: Text exercises T2.4, T2.8, T2.9 (this problem has four parts); Exercises (page 98) 2.1, 2.3, 2.7; Computer project: Computer experiment 2.2 (page 76)
6. Lecture 7, 09/20/11 Section 2.5,2.6
7. Lecture 8, 09/22/11 Sections 2.6 and 3.1
8. Lectures 9 and 10, 09/27-09/29 Sections 3.1, 3.2, 3.3

9. Homework #3, due Thursday, October 20: Text exercises T3.1, T3.5, T3.9 (You should prepare T3.1 and T3.5 for the midterm); Exercises (page 140) 3.1a-d, 3.3, 3.5, 3.10; (You should work problems 3.1 and 3.3 in preparation for the midterm) Computer project: Computer experiment 3.1 (page 109)

Other problems you might want to work in preparation for the midterm (you should not hand in these problems): page 36 #1.2 ,1.5, 1.9; page 98 #2.4, 2.11; page 140 #3.4, 3.6;
10. Lectures 11, 10/04/11 Midterm review
11. Lecture 12, 10/06/11 First midterm
12. Lecture 13, 10/13/11 Sections 3.4 and 3.5
13. Lecture 14, 10/18/11 Sections 3.5 (cont'd) and 4.1
14. Lecture 15, 10/20/11 Sections 4.1 (cont'd), 4.2, 4.3; Matlab codes: Sierpinski gasket, A map of SG, Choose random, Julia set

15. Homework #4, due Thursday, November 3: Text exercises T4.6, T4.11; page 186 #4.2, 4.5, 4.7; Computer project: Computer experiment 4.2; write a program to draw the Mandelbrot set. Bonus computer project Computer experiment 4.4;
16. Lecture 16, 10/25/11 Sections 4.2, 4.3
17. Lecture 17. 10/27/11 Section 4.4, 4.5
18. Lecture 18, 11/1/11 Sections 5.1, 5.2, 5.3
19. Lecture 19, 11/3/11 Problems, Section 5.4
20. Lecture 20, 11/8/11 Midterm review, Section 5.5, 5.6; A couple of definitions; Horseshoe map on Wikipedia
Homework #5 due Thursday, November 17: Text exercises T5.2, T5.6 (you should work problem T5.2 in preparation for the midterm); page 226 #5.4 (also preparation for the midterm), 5.6, 5.8.; Computer project: Computer experiment 5.1; Bonus computer projectComputer experiment 5.2; Important: you need to work alone on the bonus computer project in order to receive the credit!
21. Other problems you might want to work in preparation for the midterm (you should not hand in these problems): page 140 #3.6, 3.11; page 186 #4.3, 4.6, 4.8, 4.12;
22. Lecture 21, 11/10/11 Midterm

23. Final computer project: Computer Experiment 6.1 on page 236 and Computer Experiment 6.3 on page 263; You must work on your own for this computer project. The deadline is Friday, December 9, 11:59pm.
Additional problems in preparation for the final exam Text Exercises: T6.1, T6.2, T6.3, T6.6; page 266 6.1, 6.2, 6.4, 6.5, 6.8

### Matlab Info

We will use Matlab to study numerically dynamical systems. I chose Matlab because I believe that Matlab is easy and it is widely used in scientific community. Matlab should be installed on all computers from the computer lab. Here are some links to some tutorials about Matlab on the web:

### LaTeX Info

Here are some websites where you can find tutorials and information about LaTeX:

### How to install and use LaTeX

• If you are using Linux then you should install Texlive using your favorite software manager. Suggested editors are: texmaker, kile, emacs (for the power users); you can install all these editors using your favorite software manager.
• If you are using Windows then you should install Miktex; suggested editor: texmaker; there are many other Latex editors for Windows but I am not familiar with them.
• If you are using MacOSX then you should install TexShop. It comes with its own editor. You can also use texmaker.
• LyX is a user friendly interace to LaTeX that is available for Linux, MacOSX, and Windows.

### Beamer

Beamer is a special LaTeX package that you can use to create great presentations. You should be able to install easily beamer from Miktex or Texshop. If you use Linux you can install the beamer package using a software manager.