Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne
Constructing complete chaotic maps with reciprocal structures.
Constructing multi-branches complete chaotic maps that preserve specified invariant density.
Continued fractions and the Gauss map.
Continuity of the Hausdorff dimension for invariant subsets of interval maps.
Continuity of the maps and .
Continuum many tent map inverse limits with homeomorphic postcritical ω-limit sets
We demonstrate that the set of topologically distinct inverse limit spaces of tent maps with a Cantor set for its postcritical ω-limit set has cardinality of the continuum. The set of folding points (i.e. points at which the space is not homeomorphic to the product of a zero-dimensional set and an arc) of each of these spaces is also a Cantor set.
Corrigendum : “Almost sure rates of mixing for i.i.d. unimodal maps”
Coupled maps and analytic function spaces
Critical portraits for postcritically finite polynomials
We extend the work of Bielefeld, Fisher and Hubbard on critical portraits to arbitrary postcritically finite polynomials. This gives the classification of such polynomials as dynamical systems in terms of their external ray behavior.
Cycles of distance-decreasing mappings in the ring of n-adic integers
We give a description of possible sets of cycle lengths for distance-decreasing maps and isometries of the ring of n-adic integers.
Cycles of links and fixed points for orientation preserving homeomorphisms of the open unit disk
Michael Handel proved the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links at infinity. More recently, the author generalized Handel's theorem to a wider class of cycles of links. In this paper we complete this topic describing exactly which are all the cycles of links forcing the existence of a fixed point.