Off-center reflections: caustics and chaos.
On circle map coupled map lattice.
On commuting circle mappings and simultaneous Diophantine approximations.
On conjugacy equation in dimension one
In this paper, recent results on the existence and uniqueness of (continuous and homeomorphic) solutions φ of the equation φ ∘ f = g ∘ φ (f and g are given self-maps of an interval or the circle) are surveyed. Some applications of these results as well as the outcomes concerning systems of such equations are also presented.
On Kurzweil's 0-1 law in inhomogeneous Diophantine approximation
We give a necessary and sufficient condition such that, for almost all s ∈ ℝ, ||nθ - s|| < ψ(n) for infinitely many n ∈ ℕ, where θ is fixed and ψ(n) is a positive, non-increasing sequence. This can be seen as a dual result to classical theorems of Khintchine and Szüsz which dealt with the situation where s is fixed and θ is random. Moreover, our result contains several earlier ones as special cases: two old theorems of Kurzweil, a theorem of Tseng and a recent...
On some properties of orientation-preserving surjections on the circle
On the entropy for group actions on the circle
We show that for a finitely generated group of C² circle diffeomorphisms, the entropy of the action equals the entropy of the restriction of the action to the non-wandering set.
On the rotation sets for non-continuous circle maps.
On the sructure of non-singular iteration groups on the circle.
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 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.