Reading: pg. 603-639

**1.** Consider the logistic map f(x)=** a**x(1-x) with

**2.** Draw the phase portrait of the logistic map for ** a** in
(2,3). Compute three orbits for each of

**3.** Draw a staircase diagram for the logistic map for ** a**=.5,1.5,2.5,3.
Compare this with the phase portrait approach.

**4.** Sketch the phase portraits for the maps f(x)=-x, g(x)=x^3, and h(x)=x+x^2 (for all x0).
Repeat with a staircase diagram. Which fixed points, if any, are non-hyperbolic?

**5.** Use the Mean Value Theorem to prove that if p is a hyperbolic fixed point of a differentiable map
and the multiplier for p is less than one in modulus then there is an open interval U about p such that if
x0 is in U then the forward orbit of x0 converges to p.

Student-contributed MAPLE worksheet for #2,3,4. (Submitted by Bill Richardson.)

*Maintainer*: leader@rose-hulman.edu.