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We give a characterization for two different concepts of quasi-analyticity in Carleman ultraholomorphic classes of functions of several variables in polysectors. Also, working with strongly regular sequences, we establish generalizations of Watson’s Lemma under an additional condition related to the growth index of the sequence.
This paper deals with the Hausdorff dimension of the Julia set of quadratic polynomials. It is divided in two parts. The first aims to compute good numerical approximations of the dimension for hyperbolic points. For such points, Ruelle’s thermodynamical formalism applies, hence computing the dimension amounts to computing the zero point of a pressure function. It is this pressure function that we approximate by a Monte-Carlo process combined with a shift method that considerably decreases the computational...
Dans cet article, nous démontrons deux résultats. L’un concerne les séries telles que est une série algébrique. Soit cet ensemble de fonctions. Si appartient à , et si est un polynôme-exponentiel tel que est entière, alors il existe un polynôme tel que appartienne à .L’autre résultat est parallèle au premier. Soit une série algébrique à coefficients dans un corps (qui est soit , soit un corps quadratique imaginaire). Soit une série rationnelle à coefficients dans . Avec...
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