Parabolic curves for diffeomorphisms in C2.
Parabolic curves in .
Parabolic orbifolds and the dimension of the maximal measure for rational maps.
Parapuzzle of the multibrot set and typical dynamics of unimodal maps
We study the parameter space of unicritical polynomials . For complex parameters, we prove that for Lebesgue almost every , the map is either hyperbolic or infinitely renormalizable. For real parameters, we prove that for Lebesgue almost every , the map is either hyperbolic, or Collet–Eckmann, or infinitely renormalizable. These results are based on controlling the spacing between consecutive elements in the “principal nest” of parapuzzle pieces.
Pasting together Julia sets: a worked out example of mating.
Periodic points and dynamic rays of exponential maps.
Periodic points of some algebraic maps.
Perturbations of flexible Lattès maps
We prove that any Lattès map can be approximated by strictly postcritically finite rational maps which are not Lattès maps.
Pinceaux linéaires de feuilletages sur CP(3) et conjecture de Brunella.
The general element of a pencil of Cod 1 foliation in CP(3) either has an invariant surface or contains a subfoliation by algebraic curves.
Pleating coordinates for the Earle embedding
Points périodiques d’applications birationnelles de
Nous donnons une condition suffisante pour l’existence de points périodiques pour une application birationnelle de . Sous cette hypothèse, une estimation précise du nombre de points périodiques de période fixée est obtenue. Nous donnons une application de ce résultat à l’étude dynamique de ces applications, en calculant explicitement l’auto-intersection de leur courant invariant naturellement associé. Nos résultats reposent essentiellement sur le théorème de Bézout donnant le cardinal de l’intersection...
Polymorphisms and linearization of nonlinear polynomials.
Polynomial diffeomorphisms of : VII. Hyperbolicity and external rays
Polynomial diffeomorphisms of C2: currents, equilibrium measure and hyperbolicity.
Polynomial diffeomorphisms of C2. III. Ergodicity, exponents and entropy of the equilibrium measure.
Polynomial diffeomorphisms of C2. IV: The measure of maximal entropy and laminar currents.
Polynomials, Symmetry, and Dynamics: an Undertaking in Aesthetics
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.
Porosity of Julia sets of non-recurrent and parabolic Collet-Eckmann rational functions.
Preperiodic dynatomic curves for
The preperiodic dynatomic curve is the closure in ℂ² of the set of (c,z) such that z is a preperiodic point of the polynomial with preperiod n and period p (n,p ≥ 1). We prove that each has exactly d-1 irreducible components, which are all smooth and have pairwise transverse intersections at the singular points of . We also compute the genus of each component and the Galois group of the defining polynomial of .