We prove an analogue of Poincaré’s classification of circle homeomorphisms for conservative homeomorphisms of the two-torus with unique rotation vector and a certain bounded mean motion property. In particular, this provides an equivalent characterisation of the semi-conjugacy class of an irrational rotation within the space of conservative toral homeomorphisms. For minimal toral homeomorphisms...

We introduce topological definitions of expansivity, shadowing, and chain recurrence for homeomorphisms. They generalize the usual definitions for metric spaces. We prove various theorems about topologically Anosov homeomorphisms (maps that are expansive and have the shadowing property) on noncompact and non-metrizable spaces that generalize theorems for such homeomorphisms on compact metric sp...

The concept of β∗-homeomorphisms is introduced and investigated by Palanimani [13] earlier. In the present paper we investigate some more properties of β∗-homeomorphisms and also investigate contra β∗-homeomorphisms.

We give an equivalent condition for the existence of a semi-conjugacy to an irrational rotation for conservative homeomorphisms of the two-torus. This leads to an analogue of Poincaré's classification of circle homeomorphisms for conservative toral homeomor-phisms with unique rotation vector and a certain bounded mean motion property. For minimal toral homeomorphisms, the result extends to arbi...

We show that, for any n ≠ 2, most orientation preserving homeomorphisms of the sphere S2n have a Cantor set of fixed points. In other words, the set of such homeomorphisms that do not have a Cantor set of fixed points is of the first Baire category within the set of all homeomorphisms. Similarly, most orientation reversing homeomorphisms of the sphere S2n+1 have a Cantor set of fixed points for...

We study monodromies of plane curve singularities and pseudo-periodic homeomorphisms oriented surfaces with boundary using tête-à-tête graphs twists. A twist is a generalisation the classical Dehn twist. introduce class mixed twists, prove that twists contain irreducible singularities. In sequel paper, fourth author B. Sigurdsson have extended this to reducible case.

Given two points p and q of the Sierpinski universal plane curve S, necessary and/ or sufficient conditions are discussed in the paper under which there is a mapping I of S onto itself such that I(P) = q and I belongs to one of the following: homeomorphisms, local homeomorphisms, local homeomorphisms in the large sense, open, simple or monotone mappings.