Bounded homeomorphisms of the open annulus

Pseudo-rotations of the open annulus

In this paper, we study pseudo-rotations of the open annulus, i.e. conservative homeomorphisms of the open annulus whose rotation set is reduced to a single irrational number (the angle of the pseudo-rotation). We prove in particular that, for every pseudo-rotation h of angle ρ, the rigid rotation of angle ρ is in the closure of the conjugacy class of h. We also prove that pseudo-rotations are ...

Periodic Point Free Homeomorphisms of the Open Annulus: from Skew Products to Non-fibred Maps

The aim of this paper is to study and compare the dynamics of two classes of periodic point free homeomorphisms of the open annulus, homotopic to the identity. First, we consider skew products over irrational rotations (often called quasiperiodically forced monotone maps) and derive a decomposition of the phase space that strengthens a classification given by J. Stark. There exists a sequence o...

Chain Transitivity and Rotation Shadowing for Annulus Homeomorphisms

We present a relation between the rotation of chain transitive sets and the rotation shadowing for annulus homeomorphisms isotopic to identity.

On bD-Sets and Associated Separation Axioms

On the Dynamics of Homology-preserving Homeomorphisms of the Annulus

We consider the homeomorphisms of the compact annulus A = S1 × [−1, 1] isotopic to the symmetry SA which interchanges the two boundary components. We prove that if such a homeomorphism is, in some sense, conservative and twisted, then it possesses a periodic orbit of period exactly two. This can be regarded as a counterpart of the Poincaré-Birkhoff theorem in the isotopy class of SA.