We study the spectral characterization and Dirac cones, always through periodic quantum graphs, in three situations. Firstly, we model bidimensional honeycomb materials, for instance, Graphene and Boron Nitride. We consider ...

In the present work, we will do a study of linear dynamics of operators, focusing mainly on the concepts of topological transitivity, hypercyclicity and chaoticity. At rst, we will deal with non-linear dynamical systems ...

This dissertation mainly follows the works of \cite{Gr2} and \cite{Gr5}. Considering $\mathbb{K}$ a field, algebraically closed with positive characteristic, we presented invariants of singularities in $\mathbb{K}[[\u ...

Our goal in this work is to study a nonautonomous parabolic differential equation. We are going to show some results about existence of pullback attractors for this type of problem and for the equation without the delay.

This work focuses on four major themes: semiflows; generalized semiflows; invariant measure for set-valued maps; and random dynamical systems. The study of semiflows aims to understand the asymptotic behavior of solutions ...

The link between braid groups on surfaces and crystallographic groups has become such an interesting topic. In the last years some advances were found in the studies of this relation, specially in the case of Artin braid ...

The main objective of this work is to prove Tverberg-type theorems and related results. More specifically, we will present an alternative proof for the Bárány-Larman conjecture for the case $r = p-1 $ with $ p $ a prime, ...

In both the line and the circle, we shall to prove that the Cauchy problem for the ``good'' Boussinesq equation is locally well-posed in a class of Gevrey functions, which includes a class of analytic functions that can ...

This work is dedicated to study a non-autonomous formulation of the Klein-Gordon-Zakharov system, which is a coupled system consisting of two non-autonomous evolution equations, where each one is of second order in time. ...

In this work, we have two objectives: the first lives in the context of the classification, up to equivariant cobordism, of the pairs (M, T) , where M is a closed and smooth manifold and T is a smooth involution ...