Complexities of finite families of polynomials, Weyl systems, and constructions in combinatorial number theory
Résumé
We introduce two notions of complexity of a system of polynomials $p_{1},\ld,p_{r}\in\Z[n]$ and apply them to characterize the limits of the expressions of the form $\mu(A_{0}\cap T^{-p_{1}(n)}A_{1}\cap\ld\cap T^{-p_{r}(n)}A_{r})$ where $T$ is a skew-product transformation of a torus $\T^{d}$ and $A_{i}\sle\T^{d}$ are measurable sets. The obtained dynamical results allow us to construct subsets of integers with specific combinatorial properties related to the polynomial Szemer\'{e}di theorem.
Origine : Fichiers produits par l'(les) auteur(s)
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