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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....
Let be a disjoint decomposition of and let be a vector field
on , defined to be linear on each cell of the decomposition . Under
some natural assumptions, we show how to associate a semiflow to and prove that such
semiflow belongs to the o-minimal structure . In particular,
when is a continuous vector field and is an invariant subset of ,
our result implies that if is non-spiralling then the Poincaré first
return map associated is also in .
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 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 rational map. We...
Soit un difféomorphisme d’une surface possédant deux fers à cheval tels que et aient en un point une tangence quadratique isolée. Nous montrons que, si la somme des dimensions transverses de et est strictement plus grande que 1, les difféomorphismes voisins de tels que et soient stablement tangents au voisinage de forment une partie de densité inférieure strictement positive en .
We show that any transversally complete Riemannian foliation of dimension one on any possibly non-compact manifold is tense; namely, admits a Riemannian metric such that the mean curvature form of 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...
We consider iterated function systems on the interval with random perturbation. Let be uniformly distributed in [1-ε,1+ ε] and let be contractions with fixpoints . We consider the iterated function system , where each of the maps is chosen with probability . 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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