On periodic translations on <i>n</i>-torus
We consider periodic translations on n -torus and investigate the set of all conjugating homeomorphisms for topologically conjugated translations. It was shown by J. Nielsen [Dansk Videnskaternes Selskab. Math.-fys. Meddelerer, 1937, Vol.15, 1-77] that two periodic homeomorphisms of two-torus such that all points have the same period are topologically conjugate if and only if they have the same period. We consider the problem when two periodic translations on n -torus are topologically conjugate by means of toral automorphism. The main result is that two periodic translations on n -torus of the same period are topologically conjugate by means of countable family of toral automorphisms. Moreover, we show that for two periodic translations that are topologically conjugate each homotopy class in the set of all conjugating homeomorphisms contains continuum of homeomorphisms.