# Math 4973 – Chaotic Dynamical Systems

### Course Materials:

Maple Worksheets

• Approximating the square root of 5
• Orbits close to a fixed point (page 23)
• Example of a chaotic orbit for f(x) = 4x(1-x)
• Exploring the doubling function (problems 11-14 page 27)
• Example of an eventually periodic orbit for f(x) = 3.3x(1-x)
• Problem 5 from chapter 4 (page 34)
• Chapter 5 experiment (page 48)
• Chapter 5 experiment – part d(page 48)
• Problem 4 from chapter 5 (page 50)
• Chapter 6 experiment (page 63)
• Problem 1b from chapter 6 (page 67)
• Logistic equation bifurcation diagram
• Logistic equation attracing region for x=0
• Logistic equation attracing region for x=0 (more detail and orderly)
• Quadratic orbits self repeating (pages 84-87)
• Quadratic iterator – three cycles (chapter 11)
• Newtons Method (chapter 13)
• Sierpinski Gasket (fractals – chapter 14)
• Sierpinski Gasket try 2(fractals – chapter 14)
• Sierpinski Gasket try 3 (fractals – chapter 14)
• Cube contractions (fractals – chapter 14)
• Cube contractions rotating by pi/4 (fractals – chapter 14)
• Cube contractions 2 (fractals – chapter 14)
• Cube contractions 3 (fractals – chapter 14)
• Cube contractions 4 (fractals – chapter 14)
• Fractal (page 196)
• Julia Set with c=0.5
• Julia Set with c=0.5, backwards iteration
• Julia Set with c=0.255
• Julia Set with c=0.255, backwards iteration
• Julia Set with c=0.360284+0.100376i
• Julia Set with c=0.360284+0.100376i, backwards iteration
• Julia Set with c=-0.75
• Julia Set with c=-0.75, backwards iteration
• Julia Set with c=-0.75+0.1i
• Julia Set with c=-0.75+0.1i, backwards iteration
• Mandelbrot Set