Prof. Dr. Ricardo Miranda Martins

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Photo: Centre de Recerca Matemàtica, Barcelona, 2016.

CV/Research/Publications

Research

My research area is Dynamical Systems (Qualitative Theory of Differential Equations). My PhD was about reversible-equivariant dynamical systems and their bifurcations (invariant tori, limit cycles, etc). During my postdoc I started studying non-smooth dynamical systems (structural stability, limit cycles).

More recently I’m interested in the chaotic behavior of non-smooth dynamical systems and also in the properties of piecewise smooth differential equations defined on low dimensional compact manifolds. The use of techniques from dynamical systems to study geometric flows (Ricci flow) is also one of my current research topics.

Publications

  1. R. M. Martins, D. J. Tonon, The chaotic behavior of piecewise smooth differential equations on two dimensional torus and sphere, Dynamical Systems: An International Journal 34, p. 356-373, 2019.
  2. K. S. Andrade, M. R. Jeffrey, R. M. Martins, M. A. Teixeira, On the Dulac’s Problem for Piecewise Analytic Vector Fields, Journal of Differential Equations 266, p. 2259-2273, 2019.
  3. R. M. Martins, D. Tonon, J. Llibre, Limit cycles of piecewise smooth differential equations on two dimensional torus, Journal of Dynamics and Differential Equations 30, p. 1011–1027, 2018.
  4. R. M. Martins, O. Gomide, Limit cycles for quadratic and cubic planar differential equations under polynomial perturbations of small degree, Discrete and Continuous Dynamical Systems 37, p. 3353-3386, 2017.
  5. R. M. Martins, L. Grama, A brief survey on the Ricci flow in homogeneous manifolds, São Paulo Journal of Mathematical Sciences 9, p. 37-52, 2015.
  6. R. M. Martins, M. A. Teixeira, Minimal sets in double-perturbed differential equations, Houston Journal of Mathematics 41, p. 491–512, 2015.
  7. R. M. Martins, R. D. S. Oliveira, A. C. Mereu, An estimative for the number of limit cycles in a Liénard-like perturbation of a quadratic non-linear center, Nonlinear Dynamics 79, p. 185–194, 2015.
  8. R. M. Martins, A. C. Mereu, Limit cycles in discontinuous classical Lienard equations, Nonlinear Analysis: Real World Applications 20, p. 67–73, 2014.
  9. R. M. Martins, Formal Equivalence Between Normal Forms of Reversible and Hamiltonian Dynamical Systems, Communications in Pure and Applied Analysis, 13(2), p. 703–703, 2014.
  10. A. L. A. Araújo, R. M. Martins, Existence of periodic solutions for a nonautonomous differential equation, Bulletin of the Belgian Mathematical Society Simon Stevin 19, p. 305–310, 2012.
  11. L. Grama, R. M. Martins, Global behavior of the Ricci flow on homogeneous manifolds with two isotropy summands, Indagationes Mathematicae 23, p. 95–104, 2012.
  12. J. Llibre, R. M. Martins, M. A. Teixeira, On the birth of minimal sets for perturbed reversible vector fields, Discrete and Continuous Dynamical Systems, Series A 31(3), p. 763–777, 2011.
  13. R. M. Martins, M. A. Teixeira, Reversible-equivariant systems and matricial equations, Anais da Academia Brasileira de Ciências 83(2), p. 375–390, 2011.
  14. R. M. Martins, M. A. Teixeira, On the Similarity of Hamiltonian and Reversible Vector Fields in 4D, Communications in Pure and Applied Analysis, 10(4), p. 1257–1266, 2011.
  15. A. Jacquemard, R. M. Martins, Solução de sistemas algébricos e aplicações em teoria de singularidades, Revista Matemática Universitária 47 (2009) (Printed in December/2010).
  16. J. Llibre, R. M. Martins, M. A. Teixeira, Periodic orbits, invariant tori and cylinders of Hamiltonian systems near integrable ones having a return map equal to the identity, J. Math. Phys. 51, 082704, 2010.
  17. L. Grama, R. M. 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. 133(5), p. 463 – 469, 2009.

Education

Positions

Research groups on web

Students

See this page for more information. Some numbers:

Current

Former

Grants

Current

Past

Awards

No Nobel Prizes here (yet!), but I’m very proud of my awards, in special those related to teaching activities.

Services to the University

Committees/Councils/Commissions


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