In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence. ...

We present a version of the Poincare-Bendixson Theorem on the Klein bottle K(2) for continuous vector fields. As a consequence, we obtain the fact that K(2) does not admit continuous vector fields having a omega-recurrent ...

For some abstract classes of nonlinear non-autonomous systems with variable and state-dependent delays existence, non-existence and multiplicity of periodic solutions are discussed. To illustrate the efficiency of the ...

We study the probabilistic behaviour of the continued fraction expansion of a quadratic irrational number, when weighted by some "additive" cost. We prove asymptotic Gaussian limit laws, with an optimal speed of convergence. ...

The Hartman-Grobman Theorem of linearization is extended to families of dynamical systems in a Banach space X, depending continuously on parameters. We prove that the conjugacy also changes continuously. The cases of ...

Let X, Y be asymmetric normed spaces and Lc(X, Y ) the convex cone of all linear continuous operators from X to Y . It is known that in general, Lc(X, Y ) is not a vector space. The aim of this note is to give, using ...