2. Quickies. Answers only -- no partial credit.
3. Use graphical analysis to give a complete orbit analysis of the function F(x) = -x2. List all fixed points and cycles and tell if they are attracting or repelling. List all points whose orbits tend to cycles or fixed points and all points whose orbits tend to + or - infinity.
4.Definitions. Give the precise definitions of each of the following.
5.In an essay, describe the bifurcation that occurs at c = -3/4 for the family of functions Fc(x) = x2 + c. Your essay should include enough graphs and bifurcation diagrams to explain this bifurcation fully.
6. In an essay, describe the sequence space Sigma. Define the metric on Sigma. Discuss what it means for two points to be close together in Sigma. Give examples of nearby points and points that are far apart. You will be graded on the accuracy of your statements as well as the use of English in your essay (spelling, grammar, etc.)
7. Consider the subset of Sigma that consists of all sequences that have no strings of the form 0110 in them. Is this set dense? If so, prove it. If not, prove it. And, most certainly, have fun in either case.