We present an extension of the notion of infinitesimal Lyapunov function to singular flows, and from this technique we deduce a characterization of partial/sectional hyperbolic sets. In absence of singularities, we can also characterize uniform hyperbolicity. These conditions can be expressed...

All information about a symbolic dynamical system X is contained in the lan- guage L(X) of its finite blocks. In formal language theory, the syntactic semigroup of a language often plays an important role. Here we consider the syntactic semigroup S(X) of L(X), and more precisely, a finite...

In the first part of the talk there will be introduced definitions of covering and locally covering mappings. A short review of the modern results in this area (such as coincidence points theorems and perturbation theorems) will be presented. The second part of the talk is devoted to applications...

We consider a discrete dynamical system f : M → M, where M is a Riemannian manifold and f is a diffeomorphism. We assume that the dynamical system has a Gibbs- Markov-Young structure, which consists of a reference set Λ with a hyperbolic product structure that satisfies certain...

Consider the Banach manifold of real analytic linear co-cycles with values in the general linear group of any dimension and base dynamics given by a Diophantine translation on the circle. We
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We present several mathematical models for tuberculosis (TB). We apply optimal control to a specific TB mathematical model and show how this theory can help on the reduction of the number of infectious TB individuals.

We will present a class of shift-like dynamical systems and discuss an example.

Roughly speaking, a tiling is an arrangement of tiles that covers Rd without overlapping. An important class of tilings is that of self-similar tilings. In order to construct a self-similar tiling, one starts with a finite number (up to translation) of tiles and a substitution map that determines...

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There is a topological conjugation between piecewise increasing linear and piece- wise expanding interval maps. Properties of such maps can be studied through the piecewise linear case. This case has connections with number theory, e.g. the Gauss- Gegenbauer generalization of Fermat’s little...