Exponent matrices and topological equivalence of maps

Conjugate classes of continuous maps of the interval $[0,\,1]$ into itself, whose iterations form a finite group are described. For each of possible groups of iterations one to one correspondence between conjugate classes of maps and equivalent classes of $(0,\,1)$-exponent matrices of special form is constructed. Easy way of finding the quiver of the map in terms of the set of its extrema is found.