We study a liaison between the Bohl's exponents and the exponential dichotomy spectrum of a non-autonomous linear system of difference equations on the whole line Z. More specifically, we prove that for any initial condition ...

We prove that a linear nonautonomous differential system with nonuniform hyperbolicity on the half line can be written as diagonal system with a perturbation which is small enough. Moreover we show that the diagonal terms ...

In this article we introduce a nonautonomous version of the Markus-Yamabe conjecture from an exponential dichotomy spectrum point of view. We prove the validity of this conjecture for the scalar and triangular case. ...

We dicuss in this work some characterizations of the absolutely continuous spectrum of arbitrary multiplicity of discrete matrix-valued Jacobi operators on (...). Essentially, these results extend some well-known ...

In this thesis we will consider a nonautonomous linear system which admits nonuniform contraction and a nonlinear perturbation bounded at the origin. We search to establish an equivalence between the solutions of the systems ...