Currículo

Formação

2020–24   Doutorado em Matemática, IMECC, Unicamp.
Tese: Entropy in Piecewise Smooth Dynamics and Symbolic Dynamics
Orientador: Régis Varão

2018–19   Mestrado em Matemática, IMECC, Unicamp.
Dissertação: Folheações e ergodicidade de medidas transversas
Orientador: Régis Varão

2014–17   Bacharelado em Matemática, IMECC, Unicamp.
Orador da turma de Bacharelado em Matemática

Cargos

2025–   Professor Doutor I (substituto), IMECC, Unicamp, Campinas.

2025–   Professor Substituto Assistente, UNIFESP, São José dos Campos.

Didática

2025–   IMECC, Campinas.

• 2026/1ºS   Cálculo 3 (MA311)
• 2025/2ºS   Cálculo Numérico (MS211)

2025–   UNIFESP, São José dos Campos.

• 2026/1ºS   Cálculo em Uma Variável
• 2026/1ºS   Geometria Analítica
• 2025/2ºS   Cálculo em Uma Variável

2019–23   Estagiário, IMECC, Campinas — Programa de Estágio Docente (PED).

• 2023/1ºS   Cálculo I (MA111)
• 2022/2ºS   Cálculo II (MA211)
• 2022/1ºS   Cálculo I (MA111)
• 2019/2ºS   Análise I (MA502)

2015   Monitor, IMECC, Campinas — Programa de Apoio Didático (PAD).

• 2015/1ºS   Cálculo I (MA111)

Financiamentos

2020–24   Bolsa de Doutorado, CNPq.
Tese: Entropy in Piecewise Smooth Dynamics and Symbolic Dynamics

2018–20   Bolsa de Mestrado, FAPESP.
Dissertação: Folheações e ergodicidade de medidas transversas

2017–18   Bolsa de Iniciação Científica, FAPESP.
Título: Teoria ergódica e dinâmica em espaços homogêneos

2015–16   Bolsa de Iniciação Científica, FAPESP.
Título: Dinâmica simbólica - uma introdução via exemplos hiperbólicos

Produção

Artigos

1. N. Martins, P. G. Mattos, R. Varão. Folding and Metric Entropies for Extended Shifts. Journal of Dynamics and Differential Equations, 2026.
   abs bib pdf
   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.
   abs bib pdf
   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.

Pré-publicações

1. O. M. L. Gomide, P. G. Mattos, R. Varão. The Orbit Space Approach for Piecewise Smooth Vector Fields. 2026.
   abs bib pdf
   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.

Participação em Eventos

2026   International Mathematics Days V, UFV.
Palestra: Folding and Metric Entropies for Extended Shifts

2025   Afternoon's Entropy at ICMC.
Palestra: Folding and Metric Entropies for Extended Shifts

2024   XIII Workshop on Dynamical Systems (MAT80), IMECC.
Palestra: Entropy and Non-Deterministic Chaos for Piecewise Smooth Vector Fields

2026   International Mathematics Days IV, UFV.
Pôster: Folding Entropy of the Zip Shift Map

2024   DinAmicI in Rio, IMPA.
Pôster: Entropy and Non-Deterministic Chaos for Piecewise Smooth Vector Fields

2023   VII Escola Brasileira de Sistemas Dinâmicos, UFC.
Pôster: The Orbit Space Approach for Piecewise Smooth Vector Fields

2023   XII Workshop on Dynamical Systems, IBILCE.
Pôster: The Orbit Space Approach for Piecewise Smooth Vector Fields

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