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We show by a dynamical argument that there is a positive integer valued function $q$ defined on positive integer set $mathbb N$ such that $q([log n]+1)$ is a super-polynomial with respect to positive $n$ and [liminf_{nrightarrowinfty} rleft((2n+1)^2, q(n)right)<infty,] where $r( , )$ is the opposite-Ramsey number function.
We show that the Gurarij space $mathbb{G}$ has extremely amenable automorphism group. This answers a question of Melleray and Tsankov. We also compute the universal minimal flow of the automorphism group of the Poulsen simplex $mathbb{P}$ and we prov
The noncommutative Gurarij space $mathbb{mathbb{mathbb{NG}}}$, initially defined by Oikhberg, is a canonical object in the theory of operator spaces. As the Fra{i}ss{e} limit of the class of finite-dimensional nuclear operator spaces, it can be seen
We define a collection of topological Ramsey spaces consisting of equivalence relations on $omega$ with the property that the minimal representatives of the equivalence classes alternate according to a fixed partition of $omega$. To prove the associa
We establish the finiteness of periodic points, that we called Geometric Dynamical Northcott Property, for regular polynomials automorphisms of the affine plane over a function field $mathbf{K}$ of characteristic zero, improving results of Ingram.
In the present paper, we study the distribution of the return points in the fibers for a RDS (random dynamical systems) nonuniformly expanding preserving an ergodic probability, we also show the abundance of nonlacunarity of hyperbolic times that are