Everywhere chaotic homeomorphisms on manifolds and k-dimensional Menger manifolds

In this paper, we introduce a new notion of everywhere chaotic homeomorphism and we prove that any compact connected topological n-manifold (n ⩾ 2) and any compact connected k-dimensional Menger manifold (k ⩾ 1) admit everywhere chaotic homeomorphisms. All constructions of such homeomorphisms essentially rely on one-dimensional maps and the method comes from an idea of Barge and Martin (1990).