Math 4973 – Chaotic Dynamical Systems
Course Information:
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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