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Problems(1)

There exists an integer n for every disk D ⊂ Q

Source:

1/25/2011
Let QQ be a unit square in the plane: Q=[0,1]×[0,1]Q = [0, 1] \times [0, 1]. Let T:Q⟶QT :Q \longrightarrow Q be defined as follows: T(x, y) =\begin{cases} (2x, \frac{y}{2}) &\mbox{ if } 0 \le x \le \frac{1}{2};\$$2x - 1, \frac{y}{2}+ \frac{1}{2})&\mbox{ if } \frac{1}{2} < x \le 1.\end{cases} Show that for every disk D⊂QD \subset Q there exists an integer n>0n > 0 such that Tn(D)∩D≠∅.T^n(D) \cap D \neq \emptyset.
algebra unsolvedalgebra