Fractal Interpolation in Creating Prefractal Images
Fractal Newton basins.
Fractal representation of the attractive lamination of an automorphism of the free group
In this paper, we extend to automorphisms of free groups some results and constructions that classically hold for morphisms of the free monoid, i.e., the so-called substitutions. A geometric representation of the attractive lamination of a class of automorphisms of the free group (irreducible with irreducible powers (iwip) automorphisms) is given in the case where the dilation coefficient of the automorphism is a unit Pisot number. The shift map associated with the attractive symbolic lamination...
Fractal time series -- A tutorial review.
Fractalidad extrema e indeterminación clásica en sistemas dinámicos.
Fractals and the base eigenvalue of the Laplacian on certain noncompact surfaces.
Fractions continues hermitiennes et billard hyperbolique
Nous proposons de formaliser une méthode d’approximation diophantienne dans en considérant l’action de sur le demi-plan complexe. On retrouvera le thème classique de la connexion entre développement en fractions continues et flots géodésiques modélisé ici par un billard hyperbolique.
Fractions continues multidimensionnelles et lois stables
Fractions rationnelles hyperboliques p-adiques
Fragmentable mappings and CHART groups
The purpose of this note is two-fold: firstly, to give a new and interesting result concerning separate and joint continuity, and secondly, to give a stream-lined (and self-contained) proof of the fact that "tame" CHART groups are topological groups.
Fraïssé structures and a conjecture of Furstenberg
We study problems concerning the Samuel compactification of the automorphism group of a countable first-order structure. A key motivating question is a problem of Furstenberg and a counter-conjecture by Pestov regarding the difference between , the Samuel compactification, and , the enveloping semigroup of the universal minimal flow. We resolve Furstenberg’s problem for several automorphism groups and give a detailed study in the case of , leading us to define and investigate several new types...
Frame flows on manifolds with pinched negative curvature
Fredholm theory and transversality for the parametrized and for the -invariant symplectic action
We study the parametrized Hamiltonian action functional for finite-dimensional families of Hamiltonians. We show that the linearized operator for the -gradient lines is Fredholm and surjective, for a generic choice of Hamiltonian and almost complex structure. We also establish the Fredholm property and transversality for generic -invariant families of Hamiltonians and almost complex structures, parametrized by odd-dimensional spheres. This is a foundational result used to define -equivariant...
Fredholm theory of holomorphic discs under the perturbation of boundary conditions.
Free fall motion in an invariant field of forces: the 2D-case.
Frequencies of factors in Arnoux-Rauzy sequences
Frequency locking on the boundary of the barycentre set.
From elementary algebra to Bäcklund transformations
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...