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This Week

In lectures, we did sections 4.0, 4.1 and 4.2.

Reminder

Test on 10 am on Monday February 20 in WGB G 18.

Problems

2009 Q. 4

From the Class

Show that for 0\leq\mu\leq 4 the Tent Map T_\mu maps [0,1] to itself; i.e. show that T_\mu(x)\in[0,1] for all x\in[0,1].

Show that the Logistic Map and the Tent Map (for 0\leq \mu\leq 4) both have the following properties (ie. for f=T_\mu or Q_\mu):

  1. the mapping satisfies f(1/2-x)=f(1/2+x) for all x\in [0,1/2] so the mapping is symmetric about the line x=1/2.
  2. The values of f increase steadily from f(0)=0 at the left to the maximum value at x=1/2 and decrease steadily to f(1)=0. So the maps are unimodal.

 

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