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Prof. Ricardo Miranda Martins

Hello! I’m an Associate Professor in the Mathematics Department at IMECC/Unicamp (State University of Campinas).

My e-mail address is RMiranda@unicamp.br.

I was born in 1983 and my academic background is the following:

You can find some versions of my CV here: Currículo Lattes, Google Scholar, ORCiD, Web of Science.

I am currently the Director of the Institute of Mathematics, Statistics and Scientific Computing at Unicamp.

Diretoria do IMECC - Gestão 2022-2026

Teaching/Disciplinas

Notas de aula

Research and publications

Main topics of research: Qualitative Theory of Differential Equations (34Cxx, 34C07, 34C14, 34C29), Smooth dynamical systems (37Cxx), Ricci Flow (53E20), Piecewise smooth differential equations (Filippov systems) (34A36).

Papers

  1. L. Grama, R. M. Martins, M. Patrão, L. Seco, L. D. Sperança, The Projected Homogeneous Ricci Flow and its Collapses with an Application to Flag Manifolds, Monatshefte für Mathematik, 199, 483–510, 2022.
  2. G. T. Silva, R. M. Martins, Dynamics and Stability of Non-Smooth Dynamical Systems with Two Switches, Nonlinear Dynamics 108, p. 3157-3184, 2022.
  3. K. Andrade, R. M. Martins, M. Jeffrey, M. A. Teixeira, Homoclinic boundary-saddle bifurcations in nonsmooth vector fields, International Journal of Bifurcation and Chaos 32, issue 04, 2230009, 2022.
  4. M. Manzatto, D. D. Novaes, R. M. Martins, A note on Vishik’s normal form, Journal of Differential Equations 281, p. 442-458, 2021.
  5. M. Panthee, D. S. Ledesma, R. M. Martins, Experiências no ensino de matemática durante o ensino remoto emergencial na Unicamp, Professor de Matemática Online 9, Revista Eletrônica da Sociedade Brasileira de Matemática, p. 174-186, 2021.
  6. J. S. W. Lamb, M. Lima, R. M. Martins, M. A. Teixeira, J. Yang, On the hamiltonian structure of normal forms at elliptic equilibria of reversible vector fields in \(\mathbb{R}^4\), Journal of Differential Equations 269, p. 11366-11395, 2020.
  7. 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.
  8. K. S. Andrade, R. M. Martins, M. R. Jeffrey, M. A. Teixeira, On the Dulac’s Problem for Piecewise Analytic Vector Fields, Journal of Differential Equations 266, p. 2259-2273, 2019.
  9. 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.
  10. 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.
  11. 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.
  12. R. M. Martins, M. A. Teixeira, Minimal sets in double-perturbed differential equations, Houston Journal of Mathematics 41, p. 491–512, 2015.
  13. 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.
  14. R. M. Martins, A. C. Mereu, Limit cycles in discontinuous classical Lienard equations, Nonlinear Analysis: Real World Applications 20, p. 67–73, 2014.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. R. M. Martins, M. A. Teixeira, Reversible-equivariant systems and matricial equations, Anais da Academia Brasileira de Ciências 83(2), p. 375–390, 2011.
  20. 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.
  21. A. Jacquemard, R. M. Martins, Solução de sistemas algébricos e aplicações em teoria de singularidades, Revista Matemática Universitária 47 (2009) (Printed in December/2010).
  22. 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.
  23. 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.

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Contact

IMECC/Unicamp - Main building
R. Sérgio Buarque de Holanda, 651 - office #335
Cidade Universitária - Campinas - SP, 13083-859 - Brasil
(agenda)

    


I share Federico Ardila’s axioms (more info here):


Eu compartilho dos “Axiomas de Federico Ardila” (veja detalhes aqui), listados a seguir em tradução livre:


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