Show that the two descriptions of topological transitivity given in Definition 8.10 are equivalent. A COMPUTER INVESTIGATION: Use a computer program that allows the user to control the the amount of rounding in its calculations to empirically test whether or not h: [0, 1] — [0, 1] defined by h(x) = 4x (1 – x) exhibits sensitive dependence on initial conditions. An example of such a Mathematical program can be found in the Appendix.
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