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