Benito Frazao Pires

• Abstract

  This research proposal aims at broadening the scientific collaboration between Visiting Professor Udayan Darji (University of Louisville) and Professor Benito Pires (USP-Ribeirão Preto), through a long-term visit (12 months) of the first researcher. Prior and successful scientific collaboration between the involved researchers (which resulted in a submitted article and another in progress…

  Topological dynamics of linear operators, AV.EXT

• Abstract

  The first aim of this proposal is to find necessary and sufficient conditions for the occurrence of Li-Yorke chaos in the composition operator $T_f:\varphi\mapsto \varphi\circ f$ acting on $L^p(X,\mathscr{B},\mu)$, where $\mu$ is a $\sigma$-finite measure on the Banach space $X$ and $f:X\to X$ is an injective bimeasurable map. The second aim of this proposal is the construction of switch…

  Chaotic dynamical systems, AP.R

• Abstract

  The aim of this proposal is to study the dynamics of piecewise contractions f:K-K defined on a compact convex set K contained in Rn. More precisely, we are interested in findingconditions under which f is asymptotically periodic almost surely, that is, it has finitely many limit cycles whose basins of attraction form a full subset of K. With such study, we intend to generalize many result…

  Piecewise contractions defined on Rn, AP.R

(Only some records are available in English at this moment)

• Abstract

  This research proposal is an introduction to ergodic theory focusing on its applications to number theory. More specifically, it consists in studying the stochastic behaviour of the following sequences of integers {1,2,4,8,1,3,6,1,2,5,1,...}(obtained taking the first digits of {2^n} and the sequence of the digits of the decimal expansion of a real number. In this way, the project lies div…

  Invariant measures and their applications to number theory, BP.IC

• Abstract

  This research proposal approaches the theory of asymptotically stable discrete dynamical systems. In this respect, it may be divided into two parts:the first one consists of an introduction to the general theory of discrete dynamical systems whereas the second part embraces the study of spectral conditions that ensures the asymptotic stability of the system.

  Asymptotically stable discrete dynamical systems, BP.IC