Pasting together Julia sets: a worked out example of mating.
Periodic points and dynamic rays of exponential maps.
Picard Sets for Entire Functions.
Polymorphisms and linearization of nonlinear polynomials.
Polynomial cycles in algebraic number fields
Porosity of Collet–Eckmann Julia sets
We prove that the Julia set of a rational map of the Riemann sphere satisfying the Collet-Eckmann condition and having no parabolic periodic point is mean porous, if it is not the whole sphere. It follows that the Minkowski dimension of the Julia set is less than 2.
Power series and zeroes of trinomial equations.
Power series and zeroes of trinomial equations. (Summary).
Problems and solutions by the application of Julia set theory to one-dot and multi-dots numerical methods.
Prolongement de mouvements holomorphes
Proof of a Conjecture of Gross Concerning Fix-points.
Pseudo-Bessel functions and applications.
Pseudo-iteration semigroups and commuting holomorphic maps
A connection between iteration theory and the study of sets of commuting holomorphic maps is investigated, in the unit disc of . In particular, given two holomorphic maps and of the unit disc into itself, it is proved that if belongs to the pseudo-iteration semigroup of (in the sense of Cowen) then - under certain conditions on the behaviour of their iterates - the maps and commute.
Quelques résultats sur la dimension de Hausdorff des ensembles de Julia des polynômes quadratiques
This paper deals with the Hausdorff dimension of the Julia set of quadratic polynomials. It is divided in two parts. The first aims to compute good numerical approximations of the dimension for hyperbolic points. For such points, Ruelle’s thermodynamical formalism applies, hence computing the dimension amounts to computing the zero point of a pressure function. It is this pressure function that we approximate by a Monte-Carlo process combined with a shift method that considerably decreases the computational...
Regular and limit sets for holomorphic correspondences
Holomorphic correspondences are multivalued maps between Riemann surfaces Z and W, where Q̃₋ and Q̃₊ are (single-valued) holomorphic maps from another Riemann surface X onto Z and W respectively. When Z = W one can iterate f forwards, backwards or globally (allowing arbitrarily many changes of direction from forwards to backwards and vice versa). Iterated holomorphic correspondences on the Riemann sphere display many of the features of the dynamics of Kleinian groups and rational maps, of which...
Relating Hausdorff measures and harmonic measures on parabolic Jordan curves.
Remarks on iterated cubic maps.
Remarks on the simple connectedness of basins of sinks for iterations of rational maps
Remarque sur les fonctions ayant le même ensemble de Julia
Rigidity of harmonic measure
Let J be the Julia set of a conformal dynamics f. Provided that f is polynomial-like we prove that the harmonic measure on J is mutually absolutely continuous with the measure of maximal entropy if and only if f is conformally equivalent to a polynomial. This is no longer true for generalized polynomial-like maps. But for such dynamics the coincidence of classes of these two measures turns out to be equivalent to the existence of a conformal change of variable which reduces the dynamical system...