Abstract We develop a technique, pseudo-suspension, that applies to invariant sets of homeomorphisms class annulus we describe, Handel–Anosov–Katok (HAK) homeomorphisms, generalize the homeomorphism first described by Handel. Given HAK and Cantor set, pseudo-suspension yields new space combines features both original homeomorphisms. This allows us answer well known open question providing examp...

This paper is concerned with the problem of approximating a homeomorphism by piecewise affine homeomorphisms. The main result is as follows: every homeomorphism from a planar domain with a polygonal boundary to R that is globally Hölder continuous of exponent α ∈ (0, 1], and whose inverse is also globally Hölder continuous of exponent α can be approximated in the Hölder norm of exponent β by pi...

We obtain a homotopy splitting of the forget control map for controlled homeomorphisms over closed manifolds of nonpositive curvature.

We introduce the notions of weakly and strongly positively expansive (wPE and sPE, respectively) discrete dynamical systems. Both are topological generalizations of the well-known metric notion of positive expansiveness (PE). We prove that the three notions are identical on compact metrizable spaces, but not on noncompact spaces. We investigate properties of PE, wPE, and sPE dynamical systems a...