Prof. Ricardo Miranda Martins

Research & Publications

My main research topics are: Qualitative Theory of Dynamical Systems (structural stability, limit cycles, invariant tori), Reversible-Equivariant systems, Filippov systems, Ricci flow.

Publications

1. Ricardo Miranda Martins and Tiago M. P. de Abreu, Estimates for the number of limit cycles in discontinuous generalized Liénard equations, Qualitative Theory of Dynamical Systems, accepted, 2024.
2. Leonardo Cavenagui, Lino Grama and Ricardo Miranda Martins, On the dynamics of positively curved metrics on $SU(3)/T^2$ under the homogeneous Ricci flow. Matemática Contemporânea, vol. 60, pp. 3–30, 2024.
3. Lino Grama, Ricardo Miranda Martins, Mauro Patrão, Lucas Seco and Llohann D. Sperança, The Projected Homogeneous Ricci Flow and its Collapses with an Application to Flag Manifolds. Monatshefte für Mathematik, vol. 199, pp. 483–510, 2022.
4. Guilherme Tavares da Silva and Ricardo Miranda Martins, Dynamics and Stability of Non-Smooth Dynamical Systems with Two Switches. Nonlinear Dynamics, vol. 108, pp. 3157-3184, 2022.
5. Kamila da Silva Andrade, Ricardo Miranda Martins, Mike R. Jeffrey and Marco Antonio Teixeira, Homoclinic boundary-saddle bifurcations in nonsmooth vector fields. International Journal of Bifurcation and Chaos, vol. 32, iss. 04, pp. 2230009, 2022.
6. Matheus Manzatto, Douglas Duarte Novaes and Ricardo Miranda Martins, A note on Vishik’s normal form. Journal of Differential Equations, vol. 281, pp. 442-458, 2021.
7. Mahendra Panthee, Diego Sebastian Ledesma and Ricardo Miranda Martins, Experiências no ensino de matemática durante o ensino remoto emergencial na Unicamp. Professor de Matemática Online, vol. 9, pp. 174-186, 2021.
8. Jeroen S. W. Lamb, Maurício Lima, Ricardo Miranda Martins, Marco Antonio Teixeira and J. Yang, On the hamiltonian structure of normal forms at elliptic equilibria of reversible vector fields in $R^4$. Journal of Differential Equations, vol. 269, pp. 11366-11395, 2020.
9. Ricardo Miranda Martins and Durval J. Tonon, The chaotic behavior of piecewise smooth differential equations on two dimensional torus and sphere. Dynamical Systems: An International Journal, vol. 34, pp. 356-373, 2019.
10. Kamila da Silva Andrade, Ricardo Miranda Martins, Mike R. Jeffrey and Marco Antonio Teixeira, On the Dulac’s Problem for Piecewise Analytic Vector Fields. Journal of Differential Equations, vol. 266, pp. 2259-2273, 2019.
11. Ricardo Miranda Martins, Durval J. Tonon and Jaume Llibre, Limit cycles of piecewise smooth differential equations on two dimensional torus. Journal of Dynamics and Differential Equations, vol. 30, pp. 1011–1027, 2018.
12. Ricardo Miranda Martins and Otávio Gomide, Limit cycles for quadratic and cubic planar differential equations under polynomial perturbations of small degree. Discrete and Continuous Dynamical Systems, vol. 37, pp. 3353-3386, 2017.
13. Ricardo Miranda Martins and Lino Grama, A brief survey on the Ricci flow in homogeneous manifolds. São Paulo Journal of Mathematical Sciences, vol. 9, pp. 37-52, 2015.
14. Ricardo Miranda Martins and Marco Antonio Teixeira, Minimal sets in double-perturbed differential equations. Houston Journal of Mathematics, vol. 41, pp. 491–512, 2015.
15. Ricardo Miranda Martins, Regilene D. S. Oliveira and Ana Cristina Mereu, An estimative for the number of limit cycles in a Liénard-like perturbation of a quadratic non-linear center. Nonlinear Dynamics, vol. 79, pp. 185–194, 2015.
16. Ricardo Miranda Martins and Ana Cristina Mereu, Limit cycles in discontinuous classical Lienard equations. Nonlinear Analysis: Real World Applications, vol. 20, pp. 67–73, 2014.
17. Ricardo Miranda Martins, Formal Equivalence Between Normal Forms of Reversible and Hamiltonian Dynamical Systems. Communications in Pure and Applied Analysis, vol. 13, iss. 2, pp. 703–703, 2014.
18. Anderson Luis Albuquerque Araújo and Ricardo Miranda Martins, Existence of periodic solutions for a nonautonomous differential equation. Bulletin of the Belgian Mathematical Society Simon Stevin, vol. 19, pp. 305–310, 2012.
19. Lino Grama and Ricardo Miranda Martins, Global behavior of the Ricci flow on homogeneous manifolds with two isotropy summands. Indagationes Mathematicae, vol. 23, pp. 95–104, 2012.
20. Jaume Llibre, Ricardo Miranda Martins and Marco Antonio Teixeira, On the birth of minimal sets for perturbed reversible vector fields. Discrete and Continuous Dynamical Systems, Series A, vol. 31, iss. 3, pp. 763–777, 2011.
21. Ricardo Miranda Martins and Marco Antonio Teixeira, Reversible-equivariant systems and matricial equations. Anais da Academia Brasileira de Ciências, vol. 83, iss. 2, pp. 375–390, 2011.
22. Ricardo Miranda Martins and Marco Antonio Teixeira, On the Similarity of Hamiltonian and Reversible Vector Fields in 4D. Communications in Pure and Applied Analysis, vol. 108, iss. 4, pp. 1257–1266, 2011.
23. Alain Jacquemard and Ricardo Miranda Martins, Solução de sistemas algébricos e aplicações em teoria de singularidades. Revista Matemática Universitária, vol. 47, pp. 31-39, 2010.
24. Jaume Llibre, Ricardo Miranda Martins and Marco Antonio Teixeira, Periodic orbits, invariant tori and cylinders of Hamiltonian systems near integrable ones having a return map equal to the identity. J. Math. Phys., vol. 51, pp. 082704, 2010.
25. Lino Grama and Ricardo Miranda Martins, The Ricci flow of left invariant metrics on full flag manifold $SU(3)/T$ from a dynamical systems point of view. Bull. Sci. math., vol. 135, iss. 5, pp. 463 – 469, 2009.

Chapters in Proceedings

1. Ricardo Miranda Martins, Kamila da Silva Andrade and Marco Antonio Teixeira, On Degenerate Cycles in Planar Filippov Systems. Trends in Mathematics, pp. 1-5, Springer International Publishing, 2017.
2. Otávio M. L. Gomide, Marco Antonio Teixeira and Ricardo Miranda Martins, On Semi-local Structural Stability of Filippov Systems. Trends in Mathematics, pp. 83-87, Springer International Publishing, 2017.
3. Durval J. Tonon and Ricardo Miranda Martins, The Chaotic Behavior of Piecewise Smooth Dynamical Systems on Torus and Sphere, Trends in Mathematics, pp. 125-128, Springer International Publishing, 2017.

Other publications

1. Ricardo Miranda Martins, Setembro Amarelo: o que nós matemáticos temos com isso? Noticiário da Sociedade Brasileira de Matemática 35, setembro de 2021.
2. Ricardo Miranda Martins, Equações Diferenciais: Reversibilidade e Bifurcações. Tese de Doutorado, Unicamp, 2011.
3. Ricardo Miranda Martins, A Estrutura Hamiltoniana dos Campos Reversíveis em 4D. Dissertação de Mestrado, Unicamp, 2008.
4. Ricardo Miranda Martins, Algoritmos para Álgebras Associativas e de Lie. Monografia para II Jornadas de Iniciação Científica do IMPA, 2005.

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