On minimal homeomorphisms and non-invertible maps preserving foliations

摘要

We apply the decomposition theory of a manifold, elaborated by Bing and developed by Daverman, to study a decomposition space of a foliated manifold. We consider a minimal homeomorphism preserving foliation on a compact manifold. As a consequence of our main result we obtain a generalization of the result of Kolyada, Snoha and Trofimchuk concerning a minimal skew-product homeomorphism of the 2-dimensional torus. (C) 2018 Elsevier B.V. All rights reserved.