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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.