On commuting circle mappings and simultaneous Diophantine approximations.
On the rotation sets for non-continuous circle maps.
On the structure of homeomorphisms of the open annulus
Let be a without fixed point lift to the plane of a homeomorphism of the open annulus isotopic to the identity and without wandering point. We show that admits a -invariant dense open set on which it is conjugate to a translation and we study the action of on the compactly connected components of the closed and without interior set .
On the topological dynamics and phase-locking renormalization of Lorenz-like maps
The aim of this paper is twofold. First we give a characterization of the set of kneading invariants for the class of Lorenz–like maps considered as a map of the circle of degree one with one discontinuity. In a second step we will consider the subclass of the Lorenz– like maps generated by the class of Lorenz maps in the interval. For this class of maps we give a characterization of the set of renormalizable maps with rotation interval degenerate to a rational number, that is, of phase–locking...