MathDB
Piecewise linear function

Source: KöMaL A. 735

December 20, 2018
algebrafunctionunsolved

Problem Statement

For any function f:[0,1]→[0,1]f:[0,1]\to [0,1], let Pn(f)P_n (f) denote the number of fixed points of the function f(f(…f⏟n(x)… )\underbrace{f(f(\dotsc f}_{n} (x)\dotsc ), i.e., the number of points x∈[0,1]x\in [0,1] satisfying f(f(…f⏟n(x)… )=x\underbrace{f(f(\dotsc f}_{n} (x)\dotsc )=x. Construct a piecewise linear, continuous, surjective function f:[0,1]→[0,1]f:[0,1] \to [0,1] such that for a suitable 2<A<32<A<3, the sequence Pn(f)An\frac{P_n(f)}{A^n} converges.
Based on the 8th problem of the Miklós Schweitzer competition, 2018
Back to ProblemsView on AoPS