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Tail fields generated by symbol counts in measure-preserving systems

Karl Petersen, Jean-Paul Thouvenot (2004)

Colloquium Mathematicae

A finite-state stationary process is called (one- or two-sided) super-K if its (one- or two-sided) super-tail field-generated by keeping track of (initial or central) symbol counts as well as of arbitrarily remote names-is trivial. We prove that for every process (α,T) which has a direct Bernoulli factor there is a generating partition β whose one-sided super-tail equals the usual one-sided tail of β. Consequently, every K-process with a direct Bernoulli factor has a one-sided super-K generator....

Tame semiflows for piecewise linear vector fields

Daniel Panazzolo (2002)

Annales de l’institut Fourier

Let ℰ be a disjoint decomposition of ℝ n and let X be a vector field on ℝ n , defined to be linear on each cell of the decomposition ℰ . Under some natural assumptions, we show how to associate a semiflow to X and prove that such semiflow belongs to the o-minimal structure ℝ an , exp . In particular, when X is a continuous vector field and Γ is an invariant subset of X , our result implies that if Γ is non-spiralling then the Poincaré first return map associated Γ is also in ℝ an , exp .

Tan Lei and Shishikura’s example of non-mateable degree 3 polynomials without a Levy cycle

Arnaud Chéritat (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

After giving an introduction to the procedure dubbed slow polynomial mating and quickly recalling known results about more classical notions of polynomial mating, we show conformally correct pictures of the slow mating of two degree 3 post critically finite polynomials introduced by Shishikura and Tan Lei as an example of a non matable pair of polynomials without a Levy cycle. The pictures show a limit for the Julia sets, which seems to be related to the Julia set of a degree 6 rational map. We...

Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractale

Carlos Gustavo Moreira, Jean-Christophe Yoccoz (2010)

Annales scientifiques de l'École Normale Supérieure

Soit F 0 un difféomorphisme d’une surface possédant deux fers à cheval Λ , Λ ' tels que W s Λ et W u Λ ' aient en un point q une tangence quadratique isolée. Nous montrons que, si la somme des dimensions transverses de W s Λ et W u Λ ' est strictement plus grande que 1, les difféomorphismes voisins de F 0 tels que W s Λ et W u Λ ' soient stablement tangents au voisinage de q forment une partie de densité inférieure strictement positive en F 0 .

Tenseness of Riemannian flows

Hiraku Nozawa, José Ignacio Royo Prieto (2014)

Annales de l’institut Fourier

We show that any transversally complete Riemannian foliation ℱ of dimension one on any possibly non-compact manifold M is tense; namely, M admits a Riemannian metric such that the mean curvature form of ℱ is basic. This is a partial generalization of a result of Domínguez, which says that any Riemannian foliation on any compact manifold is tense. Our proof is based on some results of Molino and Sergiescu, and it is simpler than the original proof by Domínguez. As an application, we generalize some...

The absolute continuity of the invariant measure of random iterated function systems with overlaps

Balázs Bárány, Tomas Persson (2010)

Fundamenta Mathematicae

We consider iterated function systems on the interval with random perturbation. Let Y ε be uniformly distributed in [1-ε,1+ ε] and let f i ∈ C 1 + α be contractions with fixpoints a i . We consider the iterated function system Y ε f i + a i ( 1 - Y ε ) ⁿ i = 1 , where each of the maps is chosen with probability p i . It is shown that the invariant density is in L² and its L² norm does not grow faster than 1/√ε as ε vanishes. The proof relies on defining a piecewise hyperbolic dynamical system on the cube with an SRB-measure whose projection is the...

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