MathDB
Interval I=(0,1] - ISL 1976

Source:

September 20, 2010
floor functionfunctionalgebraIterationintervalIMO Shortlist

Problem Statement

Let I=(0,1]I = (0, 1] be the unit interval of the real line. For a given number a∈(0,1)a \in (0, 1) we define a map T:I→IT : I \to I by the formula if T (x, y) = \begin{cases} x + (1 - a),&\mbox{ if } 0< x \leq a,\\ \text{ } \\ x - a, & \mbox{ if } a < x \leq 1.\end{cases}
Show that for every interval J⊂IJ \subset I there exists an integer n>0n > 0 such that Tn(J)∩J≠∅.T^n(J) \cap J \neq \emptyset.
Back to ProblemsView on AoPS