On the sructure of non-singular iteration groups on the circle.
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 structure of minimal attraction centers of recurrent trajectories of continuous maps of the interval.
On the structure of the totally ordered set of unimodal cycles.
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...
On the topology of solenoidal attractors of the cylinder
On the transitive and -limit points of the continuous mappings of the circle
We extend the recent results from the class of continuous maps of the interval to the class of continuous maps of the circle. Among others, we give a characterization of -limit sets and give a characterization of sets of transitive points for these maps.
On topological sequence entropy and chaotic maps on inverse limit spaces.
On uniformly quasisymmetric groups of circle diffeomorphisms.
On unimodal maps with critical order 2 + ε
It is proved that a smooth unimodal interval map with critical order 2 + ε has no wild attractor if ε >0 is small.
One dimensional dynamics and factors of finite automata
One-dimensional and two-dimensional dynamics of cubic maps.
Orderings of the rationals and dynamical systems
This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into three parts. The first one is mainly expository and consists in a critical review of rather standard topics such as Stern-Brocot and Farey trees and their connections with continued fraction expansion and the question mark function. In the second part we introduce two classes of (invertible and non-invertible)...
Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches
This work contributes to classify the dynamic behaviors of piecewise smooth systems in which border collision bifurcations characterize the qualitative changes in the dynamics. A central point of our investigation is the intersection of two border collision bifurcation curves in a parameter plane. This problem is also associated with the continuity breaking in a fixed point of a piecewise smooth map. We will relax the hypothesis needed in [4] where...