Rational Misiurewicz maps for which the Julia set is not the whole sphere
We show that Misiurewicz maps for which the Julia set is not the whole sphere are Lebesgue density points of hyperbolic maps.
Rational periodic points for degree two polynomial morphisms on projective space
Real and imaginary parts of polynomial iterates.
Recurrence of entire transcendental functions with simple post-singular sets
We study how the orbits of the singularities of the inverse of a meromorphic function determine the dynamics on its Julia set, at least up to a set of (Lebesgue) measure zero. We concentrate on a family of entire transcendental functions with only finitely many singularities of the inverse, counting multiplicity, all of which either escape exponentially fast or are pre-periodic. For these functions we are able to decide whether the function is recurrent or not. In the case that the Julia set is...
Regularization of currents and entropy
Remarque sur les fonctions ayant le même ensemble de Julia
Repelling periodic points and landing of rays for post-singularly bounded exponential maps
We show that repelling periodic points are landing points of periodic rays for exponential maps whose singular value has bounded orbit. For polynomials with connected Julia sets, this is a celebrated theorem by Douady, for which we present a new proof. In both cases we also show that points in hyperbolic sets are accessible by at least one and at most finitely many rays. For exponentials this allows us to conclude that the singular value itself is accessible.
Reversible complex Hénon maps.
Rigidité de quelques groupes de germes de difféomorphismes.
Using the description of non solvable dynamics by Nakai, we give in this paper a new proof of the rigidity properties of some sub-groups of Diff(C, O). The Cinfinity case is also considered here.