Homeworks 6 & 7 are below.

Homework 6:

Read chapter 4, pages 144-177

Checkout Let f : R->R be a differentiable map.
Assume 0 is a sink and

(-1,1) is the largest interval that lies entirely inside the basin of 0.

(a) What are the possible trajectories of the points -1 and 1?

(b) What are the possible Lyapunov numbers for each of -1, 0, 1?

T4.1 p. 153

T4.2 p. 155

T4.6 p. 162

T4.9 p. 177 + Addition to T4.9: Describe 3-dimensional versions of

the attractors in figures 4.3, 4.4 and 4.5 and calculate the dimension

of these versions. In figure 4.3 there are a couple of ways of

extending the example that you might choose.

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Homework 7:

Finish reading chapter 4, pages 177-182 and Lab Visit 4, 188-191.

Read chapter 5, pages 193-207.

T4.10 p. 179

E4.10 p. 187

E4.11 p. 187

E5.1 p. 226

Computer Experiment 5.2 p.202 + Also compute the
Lyapunov

dimensions for the maps given in computer experiment 5.2. Explain

your calculations. Hints:

-It says to "write a program", but you can just use Dynamics.

-The commands you need are L (set to 2), then LL, then T

-For the Tinkerbell map some of the parameters may need to

be changed, you can do this using the parameter menu PM