Bruno Rodrigues de Freitas
Bruno Rodrigues de Freitas
Institute of Mathematics and Statistics - Federal University of Goiás
Contact info:
Jacarandá street, Campus Samambaia, CP 74690-900, Goiânia, Goiás, Brazil
email: freitasmat@ufg.br
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Welcome! Here is a brief bio: I completed my degree (2005-2008), master's (2009-2010), and doctorate (2012-2016) at the Federal University of Goiás, in the Institute of Mathematics and Statistics. I completed a postdoc at Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto-USP-Brasil in 2022. I am currently a professor at the Federal University of Goiás, in the Institute of Mathematics and Statistics.
Research and Publications
Research and Publications
Research interests
Research interests
My primary research interest is concentrated in dynamical systems and differential equations of geometry. My main lines of research are the following:
Binary differential equations
Limit cycles of polynomial vector fields
Local and global bifurcations and structural stability
Non-smooth dynamic systems
Singular perturbation theory
Publications list
Publications list
[ 13] CARVALHO, TIAGO ; GONCALVES, L. F. ; DE FREITAS, BRUNO R. Geometric singular perturbation on a positive measure minimal set of a planar piecewise smooth vector field. Nonlinear Analysis-Hybrid Systems, 2025.
[ 12 ] Gerardo Anacona Erazo ; FREITAS, B. R. ; SALO, J. L. Centers of cubic polynomial differential systems. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2025.
[ 11 ] ANACONA, G. H. ; LLIBRE, JAUME ; FREITAS, BRUNO RODRIGUES On the limit cycles bifurcating from the periodic orbits of a Hamiltonian system. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 35, p. 2550040-1-2550040-8, 2025.
[ 10 ] CARVALHO, T. ; GONCALVES, L. F. ; FREITAS, BRUNO RODRIGUES Singularly perturbed Hopf boundary equilibrium of planar piecewise smooth vector fields. JOURNAL OF DIFFERENTIAL EQUATIONS, v. 440, p. 113454, 2025.
[ 9 ] DE FREITAS, BRUNO R.; FERREIRA, S. C. S. ; MEDRADO, JOAO C. Invariant manifolds of 3D piecewise vector fields. JOURNAL OF DIFFERENTIAL EQUATIONS, v. 435, p. 113313, 2025.
[ 8 ] DONIZETE, R. E. ; FREITAS, B. R. PERIODIC ORBITS IN PIECEWISE RICCATI VECTOR FIELDS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 28, p. 4325-4343, 2023.
[ 7 ] CARVALHO, TIAGO ; FREITAS, BRUNO RODRIGUES . The local behavior around switching planes in a mathematical model to chemoimmunotherapy. Communications in Nonlinear Science and Numerical Simulation, v. 120, p. 107186-107199, 2023.
[ 6 ] CRISTIANO, R. ; FREITAS, B. R. ; MEDRADO, J. C. R. Three Crossing Limit Cycles in a 3D-Filippov System Having a T -Singularity. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 32, p. 2250006-1-2250006-17, 2022.
[ 5 ] MEDRADO, J. C. R. ; DE FREITAS, BRUNO R. On the existence of limit cycles and invariant surfaces for sewing piecewise linear differential systems on R3. PHYSICA D-NONLINEAR PHENOMENA, v. 442, p. 133545, 2022.
[ 4 ] CARVALHO, T. ; FREITAS, B. R. Birth of isolated nested cylinders and limit cycles in 3D piecewise smooth vector fields with symmetry. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, v. 30, p. 2050098-1-2050098-10, 2020.
[ 3 ] CARVALHO, T. ; FREITAS, B. R. Birth of an arbitrary number of T-singularities in 3D piecewise smooth vector fields. Discrete & Continuous Dynamical Systems - B, v. 24, p. 4851-4861, 2019.
[ 2 ] FREITAS, BRUNO R; GARCIA, RONALDO A . Inflection points on hyperbolic tori of S3. QUARTERLY JOURNAL OF MATHEMATICS, v. 69, p. 709-728, 2018.
[ 1 ] DE FREITAS, BRUNO R.; LLIBRE, JAUME ; MEDRADO, JOAO C. Limit cycles of continuous and discontinuous piecewise-linear differential systems in R3. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, v. 338, p. 311-323, 2018.
Submitted manuscripts
Submitted manuscripts
Limit cycles from a monodromic infinity in R3 piecewise linear systems with concurrent tangent lines - Samuel Ferreira and João Medrado [under review]
Limit cycles in a class of piecewise polynomial differential systems having the unit circle as their switching manifold - Ronaldo Garcia and Luiz Goncalves [under review]
Limit cycles of continuous-discontinuous piecewise differential systems formed by two Hamiltonian systems and separated by a non-regular line - Deysquele Ávila, Fernanda Becatti, Jaume Llibre [under review]
Time symmetry limit cycle of 3D piecewise vector fields - Samuel Ferreira and João Medrado [under review]
Coming soon
Coming soon
Geometric singular perturbation on a reversible system - Durval Tonon and Warley Batista [submission soon]
Analysis in a discontinuous system for cancer virotherapy - Gerardo Anacona [submission soon]
Spherical curves with curvature proportional to height function - Miriam Furtado and Hiuri Reis [submission soon]
Geometric singular perturbation in 3D - Tiago Carvalho and Luiz Goncalves [submission soon]
Critical periods for some polynomial differential systems - Joan Torregrosa
Limit cycles of a continuous-discontinuous piecewise differential systems - Fernanda Becatti
Co-authors (click to open)
João Carlos Medrado, Unesp - Brazil [current]
Tiago Carvalho, Unesp - Brazil [current]
Jaume Llibre, UAB - Spain [current]
Ronaldo Garcia, UFG - Brazil [current]
Rony Cristiano, UFG - Brazil [current]
Rodrigo Euzébio, UFG - Brazil [current]
Samuel Ferreira, UFG - Brazil [current]
Luiz Goncalves, UFG - Brazil [current]
Gerardo Anacona, UFG - Brazil [current]
Joan Torregrosa, UAB - Spain [current]
Miriam Furtado, UFG - Brazil [current]
Hiuri Reis, UFG - Brazil [current]
Deysquele Ávila, UFG - Brazil [current]
Fernanda Becatti, UFG - Brazil [current]
Durval Tonon, UFG - Brazil [current]
Warley Batista, UFG - Brazil [current]
Projects
Projects
Current granted projects
Current granted projects
International Scientific, Technological and Innovation Research Projects - post-doc
Coordination: Prof. Dr. Bruno Rodrigues de Freitas
Title: Critical periods in planar polynomial centers and rigid systems
Period: 2026
International partner: Universitat Autònoma de Barcelona - Spain
Research supported by: National Council for Scientific and Technological Development
Former student projects
Master degree
Miriam Cristina Ferreira Furtado. Curvas Esféricas com Curvatura Proporcional a Função Altura, 2024
Fernanda dos Anjos Félix. Ciclos limites de grande amplitude, 2023.
Directions to the Institute of Mathematics and Statistics
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