Pedro G. Mattos

Education

Positions

Publications

Articles

1. N. Martins, P. G. Mattos, R. Varão. Folding and Metric Entropies for Extended Shifts. Journal of Dynamics and Differential Equations, 2026.  
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   In this paper we calculate the metric and folding entropies for a family of non-invertible symbolic dynamical systems $(\Sigma_{m_-,m_+}, \sigma_\phi)$ which generalizes the standard bilateral Bernoulli shifts. The space $\Sigma_{m_-,m_+}$ consists of symbolic sequences over two distinct finite alphabets, with dynamics governed by a shift map $\sigma_\phi$ incorporating a non-invertible function $\phi$ that maps one of the alphabets to the other one. These systems are, for instance, particularly useful for encoding the many-to-one baker's transformation endomorphisms, and they can also be seen as a skew product with a unilateral Bernoulli shift on the base.

2. R. D. Euzébio, P. G. Mattos, R. Varão. Characterization of Non-deterministic Chaos in Two-dimensional Non-smooth Vector Fields. Differential Equations and Dynamical Systems, 2025.  
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   Our context is Filippov systems defined on two-dimensional manifolds having a finite number of tangency points. We prove that topological transitivity is a necessary and sufficient condition for the occurrence of non-deterministic chaos when the Filippov system has non-empty sliding or escaping regions. A fundamental result for continuous flows is the equivalence of topological transitivity and existence of a dense orbit. We prove in our setting that topological transitivity for Filippov systems is indeed equivalent to the existence of a dense Filippov orbit, although, in contrast to the continuous case, we are not able to guarantee that the dense orbit implies the existence of a residual set of dense orbits. Finally, we prove that, in this context, topological transitivity implies strictly positive topological entropy for the Filippov system. This calculation is made using techniques similar to those from symbolic dynamics.

Preprints

1. O. M. L. Gomide, P. G. Mattos, R. Varão. The Orbit Space Approach for Piecewise Smooth Vector Fields. 2026.  
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   In this work we develop a well-defined theory of orbit spaces for piecewise smooth vector fields (PSVFs). This approach is inspired by the techniques already used in the study of endomorphisms, namely inverse limit analysis, and has been used before for PSVFs. We then apply the construction of our theory to understanding transitivity in PSVFs. Our results prove that the known examples of transitive PSVFs in the literature, the bean model and the sphere model, are indeed transitive in the orbit space.

Publications in other areas

1. P. G. Mattos, F. A. M. Mattos. Hiperconcentração da renda e da riqueza: como medir e por que é importante ampliar a discussão além do aspecto econômico. Revista Simetria, 2023.  
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   O artigo propõe uma discussão interdisciplinar e multidimensional da desigualdade, destacando a necessidade de unir análise qualitativa da crescente desigualdade econômica que vem ocorrendo nos países desenvolvidos com uma análise dos desdobramentos dessa desigualdade econômica sobre outras formas de manifestação de desigualdades, como a desigualdade social, ambiental, urbana entre outras. Na última seção é incorporada uma discussão sobre Urbanismo e as formas de disputa em torno dos espaços das cidades e do orçamento público.

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