Below you can find more information about my Research (research interests, papers, and working groups), my Teaching page (courses and didactic materials), and my Notes, where I post general mathematical notes.
Research
My research is in the area of Dynamical Systems, focusing on piecewise smooth dynamics, entropy, and symbolic dynamics. On this page I list my published articles and preprints, my research projects, the research groups I participate in, and a list of collaborators and colleagues.
Projects
- Non-deterministic Chaos in Piecewise Smooth Dynamical Systems
- Study of the dynamics and entropy of Filippov vector fields via the orbit space — a quotient space on which the flow is deterministic and the classical tools of ergodic theory apply.
- Entropy in Extended Symbolic Shifts
- Generalization of Bernoulli shifts to non-invertible systems with two distinct alphabets, with explicit computation of the metric and folding entropies.
Recent work
- N. Martins, P. G. Mattos, R. Varão. Folding and Metric Entropies for Extended Shifts. Journal of Dynamics and Differential Equations, 2026.
- O. M. L. Gomide, P. G. Mattos, R. Varão. The Orbit Space Approach for Piecewise Smooth Vector Fields. Preprint, 2026.
- 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.
Teaching
On this page I list the courses I have taught or am currently teaching, with didactic materials available on each course page.
Notes
Here I post general mathematical notes — expository, study, or reference — without any commitment to rigor or completeness.