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Some dynamical properties of S-unimodal maps

Tomasz Nowicki (1993)

Fundamenta Mathematicae

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

Józef Myjak, Tomasz Szarek (2003)

Bollettino dell'Unione Matematica Italiana

Let K be a compact quasi self-similar set in a complete metric space X and let M 1 K denote the space of all probability measures on K , endowed with the Fortet-Mourier metric. We will show that for a typical (in the sense of Baire category) measure in M 1 K the lower concentration dimension is equal to 0 , while the upper concentration dimension is equal to the Hausdorff dimension of K .

Spaces of ω-limit sets of graph maps

Jie-Hua Mai, Song Shao (2007)

Fundamenta Mathematicae

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.

Stretching the Oxtoby-Ulam Theorem

Ethan Akin (2000)

Colloquium Mathematicae

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

François Laubie (2000)

Journal de théorie des nombres de Bordeaux

L’étude des systèmes dynamiques non archimédiens initiée par J. Lubin conduit à déterminer la ramification de séries à coefficients dans un corps fini k , qui commutent entre elles pour la loi . Dans cet article nous traitons le cas des sous-groupes abéliens de t + t 2 k [ [ t ] ] qui correspondent par le foncteur corps de normes aux extensions abéliennes des extensions finies de p , dont la ramification se stabilise dès le début.

Szpilrajn type theorem for concentration dimension

Jozef Myjak, Tomasz Szarek (2002)

Fundamenta Mathematicae

Let X be a locally compact, separable metric space. We prove that d i m T X = i n f d i m L X ' : X ' i s h o m e o m o r p h i c t o X , where d i m L X and d i m T X stand for the concentration dimension and the topological dimension of X, respectively.

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