Aldo Portela

Dynamics of annulus maps III: periodic points and completeness

Consider a continuous surjective self map of the open annulus with degree d > 1. It is proved that the number of Nielsen classes of periodic points is the maximum possible whenever f has a completely invariant essential continuum. The same result is obtained in negative degree and for just forward invariant essential continua, provided that the continuum is locally connected. We also deal with the problem of whether there is a representative of each Nielsen class in the filled set of the invariant continuum. Moreover, if the map extends continuously to the boundary of the annulus and both boundary components are either attracting or repelling, the hypothesis on the existence of the invariant continuum is no longer needed for obtaining all the periodic points in the interior of the annulus.

On the minimality of locally similar Cantor sets of S1

In this paper we prove that if a locally similar Cantor set is under the conditions of McDuffs conjecture then it cannot be C1+?-minimal, for any ? > 0.

An example of a map which is

The aim of this work is to exhibit an example of an endomorphism of

C^2

\T^{2}

-robustly transitive but not

which is

C^1

C^2

-robustly transitive

-robustly transitive but not

Prediction of the bottled propane gas sales using a neural network-based model

C^1

C 1 STABLE MAPS: EXAMPLES WITHOUT SADDLES.

-robustly transitive.

Dynamics of annulus maps II: Periodic points for coverings

This work presents an application of the artificial neural networks ANN in the prediction of the time series of the weekly wholesale of bottled propane gas 13 kg bottles. For this purpose, several networks with different topologies were built. Many schemas of ensembles were applied to reduce prediction of errors. Additionally, given the scarce data available, it was mandatory to minimise the input dimensionality of the networks and to do this, with a rational and systematic approach, considerations about stochastic dynamical systems were made and generalisations of the Takens-Manes theorem for non-deterministic systems were used.