Sand pile automata
S-integer dynamical systems: periodic points.
Solution complète au problème de Siegel de linéarisation d'une application holomorphe au voisinage d'un point fixe
Some dynamical properties of S-unimodal maps
We study 1) the slopes of central branches of iterates of S-unimodal maps, comparing them to the derivatives on the critical trajectory, 2) the hyperbolic structure of Collet-Eckmann maps estimating the exponents, and under a summability condition 3) the images of the density one under the iterates of the Perron-Frobenius operator, 4) the density of the absolutely continuous invariant measure.
Some generic properties of concentration dimension of measure
Let be a compact quasi self-similar set in a complete metric space and let denote the space of all probability measures on , endowed with the Fortet-Mourier metric. We will show that for a typical (in the sense of Baire category) measure in the lower concentration dimension is equal to , while the upper concentration dimension is equal to the Hausdorff dimension of .
Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point
Spaces of ω-limit sets of graph maps
Let (X,f) be a dynamical system. In general the set of all ω-limit sets of f is not closed in the hyperspace of closed subsets of X. In this paper we study the case when X is a graph, and show that the family of ω-limit sets of a graph map is closed with respect to the Hausdorff metric.
Spectra of finitely generated Boolean flows.
Stability of rotation pairs of cycles for the interval maps.
Stretching the Oxtoby-Ulam Theorem
On a manifold X of dimension at least two, let μ be a nonatomic measure of full support with μ(∂X) = 0. The Oxtoby-Ulam Theorem says that ergodicity of μ is a residual property in the group of homeomorphisms which preserve μ. Daalderop and Fokkink have recently shown that density of periodic points is residual as well. We provide a proof of their result which replaces the dependence upon the Annulus Theorem by a direct construction which assures topologically robust periodic points.
Substitutions commutatives de séries formelles
L’étude des systèmes dynamiques non archimédiens initiée par J. Lubin conduit à déterminer la ramification de séries à coefficients dans un corps fini , qui commutent entre elles pour la loi . Dans cet article nous traitons le cas des sous-groupes abéliens de qui correspondent par le foncteur corps de normes aux extensions abéliennes des extensions finies de , dont la ramification se stabilise dès le début.
Sur les dynamiques holomorphes non linéarisables et une conjecture de V. I. Arnold
Systèmes dynamiques topologiques I. Étude des limites de cobords
Szpilrajn type theorem for concentration dimension
Let X be a locally compact, separable metric space. We prove that , where and stand for the concentration dimension and the topological dimension of X, respectively.