Far from equilibrium computation and particle swarm optimization.
Farey curves.
Fatou components whose boundaries have a common curve
We show that the Fatou components of a certain transcendental entire function have a common curve in their boundaries.
Fatou maps in dynamics.
Feigenbaum-Coullet-Tresser universality and Milnor's hairiness conjecture.
Feuilletages singuliers de codimension un, groupoïde de Galois et intégrales premières
Dans cet article, nous étudions le groupoïde de Galois d’un germe de feuilletage holomorphe de codimension un. Nous associons à ce -groupoïde de Lie un invariant biméromorphe : le rang transverse. Nous étudions en détails les relations entre cet invariant, l’existence de suites de Godbillon-Vey particulières et l’existence d’une intégrale première dans une extension fortement normale du corps différentiel des germes de fonctions méromorphes. Nous obtenons ainsi une généralisation d’un théorème...
Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups
We prove fibration theorems on compact Kähler manifolds with conditions on first cohomology groups of fundamental groups with respect to unitary representations into Hilbert spaces. If the fundamental group T of compact Kähler manifold X violates Property (T) of Kazhdan’s, then for some unitary representation . By our earlier work there exists a -closed holomorphic 1-form with coefficients twisted by some unitary representation , possibly non-isomorphic to . Taking norms we obtains a positive...
Finite determinacy of dicritical singularities in
For germs of singularities of holomorphic foliations in which are regular after one blowing-up we show that there exists a functional analytic invariant (the transverse structure to the exceptional divisor) and a finite number of numerical parameters that allow us to decide whether two such singularities are analytically equivalent. As a result we prove a formal-analytic rigidity theorem for this kind of singularities.
Fixed points and periodic points of semiflows of holomorphic maps.
Flat 3-webs of degree one on the projective plane
The aim of this work is to study global -webs with vanishing curvature. We wish to investigate degree foliations for which their dual web is flat. The main ingredient is the Legendre transform, which is an avatar of classical projective duality in the realm of differential equations. We find a characterization of degree foliations whose Legendre transform are webs with zero curvature.
Foliations with Degenerate Gauss maps on
We obtain a classification of codimension one holomorphic foliations on with degenerate Gauss maps.
Fonctions et feuilletages Levi-Flat. Étude locale
We define the notion of CR equivalence for Levi-flat foliations and compare in a local setting these foliations to their linear parts. We study also the situation where the foliation has a first integral ; a condition is given so that this integral is the real part of a holomorphic function.
Fractal Newton basins.
Fractalidad extrema e indeterminación clásica en sistemas dinámicos.
Fractals and the base eigenvalue of the Laplacian on certain noncompact surfaces.
Fractions rationnelles hyperboliques p-adiques
From Newton’s method to exotic basins Part I: The parameter space
This is the first part of the work studying the family of all rational maps of degree three with two superattracting fixed points. We determine the topological type of the moduli space of and give a detailed study of the subfamily consisting of maps with a critical point which is periodic of period 2. In particular, we describe a parabolic bifurcation in from Newton maps to maps with so-called exotic basins.
From Newton's method to exotic basins Part II: Bifurcation of the Mandelbrot-like sets
This is a continuation of the work [Ba] dealing with the family of all cubic rational maps with two supersinks. We prove the existence of the following parabolic bifurcation of Mandelbrot-like sets in the parameter space of this family. Starting from a Mandelbrot-like set in cubic Newton maps and changing parameters in a continuous way, we construct a path of Mandelbrot-like sets ending in the family of parabolic maps with a fixed point of multiplier 1. Then it bifurcates into two paths of Mandelbrot-like...