Ricardo Miranda Martins in research grants and scholarships supported by FAPESP.
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This project concerns the application of the Institutional Technical Funding of the Institute of Mathematics, Statistics and Scientific Computing - IMECC, UNICAMP. We propose to use these resources to replace one of the 3 machines of the Air Conditioning System of the Library of the Institute (IMECC, Unicamp) (AU)
In this project, we will continue to study piecewise smooth dynamical systems that are defined in compact manifolds. While the local theory of piecewise smooth dynamical systems is in a fairly advanced stage, the same cannot be said about its global properties. The main aim of this project is to study (i) the existence of periodic orbits and other invariant sets and (ii) the establishment…
The main aim of this project is to study global phenomena in piecewise smooth dynamical systems, continuing some recent works developed by the proponent. Among the main topics to be studied are (i) the existence of limit cycles in piecewise smooth dynamical systems defined on compact manifolds, (ii) the existence of Poincaré-Hopf-like theorems for pseudo-equilibria and (iii) the appearanc…
In this project we study the existence of minimal invariant sets in non-smooth dynamical systems. In particular, we are interested in the existence of limit cycles and homoclinic cycles in dimensions $2$ and $3$.In dimension $2$ we focus on the existence of homoclinic cycles for non-smooth systems with two zones, considering the cases saddle-focus and saddle-center (real and virtual). We …
The theory of Non-Smooth Dynamical Systems is a subject that has been developing very fast in recent years, mainly due to its strong relationship with other fields of science. Establish clear notions of stability and bifurcations that are consistent with the real world has been an arduous and challenging task for mathematicians, physicists and engineers. There is very little done with re…
In this project, we study piecewise smooth dynamical systems using the Filippov convention. Our focus will be on dynamical systems defined in low dimensional compact manifolds. We are interested in the existence of minimal sets for these systems. Moreover, we want to classify such systems in termos of the chaotic behavior. In particular, we will study the global dynamics of piecewise smoo…
In this project we will investigate the foundations of ergodic theory, with the aim of applying it to number theory problems. The two main theoretical results we will examine are the Poincaré Recurrence Theorem and the Ergodic Theorem. The methods and theorems studied will be applied to results on density of primes and to Weyls Theorem.(AU)
In this project, we will study families of piecewise smooth differential equations defined on compact two-dimensional manifolds $M$. Our main objective is to exhibit conditions for a piecewise polynomial system defined in $M$ to admit periodic orbits in cases where $M$ is the sphere or the torus. We will also study the structural stability in the case of piecewise smooth differential equa…
The aim of this project is to study systems of piecewise smooth differential equations in dimension 3, locally and globally (in $\mathbb R^3$ and also in compact manifolds). The expected results are about structural stability and chaotic behavior of these systems. Moreover, we want to study the relations between Sotomayor-Teixeira Regularization and Singular Perturbation Theory problems a…
In this project we will study the main theorem on structural stability for piecewise smooth dynamical systems on low dimensions. In particular, we will consider the global dynamics of families of piecewise smooth dynamical systems on torus $\mathbb R^2$, where the quantity of fold points have serious implications about the structural stability of the system. Moreover, on spheres $S^k$, $k…
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The study of the limit cycles is one of the most important objectives in the qualitative theoryof the planar ordinary differential equations. We remark that to obtain an upper bound for themaximum number of limit cycles for a given differential system in the plane R2, in general, is a very difficult problem. The study of the discontinuous piecewise differential systems, morerecently also …
In this project the student will spend 6 months at Imperial College, London/England, working with Prof. Jeroen Lamb. The main objective is to discuss results related to two papers in order increase his knowledge in the area of discontinuous systems and reversible systems. In addition, the student will be able to take advantage of the scientific environment of Imperial College London to ga…
| 2 / 2 | Ongoing research grants |
| 3 / 3 | Completed research grants |
| 2 / 2 | Ongoing scholarships in Brazil |
| 10 / 10 | Completed scholarships in Brazil |
| 1 / 1 | Ongoing scholarships abroad |
| 1 / 1 | Completed scholarships abroad |
| 19 / 19 | All research grants and scholarships |
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