AN EXAMPLE OF A PARTIALLY ORDERED SHARKOVSKY SPACE

Let f:R.rarw.R be a continuous function on the real line R, and denote the n-th iterate of f by f$^{n}$ :f$^{1}$=f and f$^{n}$ =f.f$^{n-1}$ for n>1. A point x.mem.R is a periodic point of f of period k>0 if f$^{k}$ (x)=x but f$^{i}$ (x).neq.x for all 01, then it must also have a fixed point, by the intermediate Theorem. Also the question has an intriguing answer which was found by ths Russian mathematician Sharkovky [6] in 1964.