Vários aspectos da dinâmica discreta

Abstract

During the period of the project, we studied several problems related to the theory of discrete dynamical systems and its connections with number theory, probability theory, and operator theory. More precisely, the project was focused on dynamical properties of p-adic and linear systems- that is dynamical systems over the space of p-adic integers/numbers and Banach spaces-, on the characterization of stochastic adding machines and its connections with Julia sets and on elimination problems in combinatorial algorithms. This study involved the following thematics: • Dynamical properties as shadowing and stability of non-invertible dynamics in the space of p-adic integers Zp and p-adic numbers Qp, where p ≥ 2 is a prime integer. • Lipschitz structural stability and shadowing of a class of homeomorphisms in complete metric spaces as Banach spaces of infinite dimension. • Stochastic adding machines and exotic Julia sets. • The introduction of a randomized version of the Josephus problem and the characterization of the limit distribution of the winning probabilities for the players in this randomized context. As a consequence of these investigations, we obtained various results which are organized in the form of the papers [7] and [1]. The papers [16] and [8] are in the final stage of writing and soon will be submitted for publication.