11 citations · 24 across the 17 of their papers we have counts for
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Sharp estimates for the number of limit cycles in discontinuous generalized Liénard equations
Tiago M. P. de Abreu, Ricardo Miranda Martins
In this paper, we study the maximum number of limit cycles for the piecewise smooth system of differential equations $\dot{x}=y, \ \dot{y}=-x-\varepsilon \cdot (f(x)\cdot y +{\rm s…
Poincaré-Hopf Theorem for Filippov vector fields on 2-dimensional compact manifolds
Joyce A. Casimiro, Ricardo M. Martins, Douglas D. Novaes
The Poincaré-Hopf Theorem relates the Euler characteristic of a 2-dimensional compact manifold to the local behavior of smooth vector fields defined on it. However, despite the imp…
On the existence of closed trajectories and pseudo-trajectories for a family of third order differential equations
Mayara Duarte de Araujo Caldas, Ricardo Miranda Martins
The goal of this article is to study the existence of closed trajectories for the differential equation in two…
Limit cycles for classes of piecewise smooth differential equations separated by the unit circle
Mayara Duarte de Araujo Caldas, Ricardo Miranda Martins
In this article we study the existence of limit cycles in families of piecewise smooth differential equations having the unit circle as discontinuity region. We consider families p…
Dynamics and Stability of Non-Smooth Dynamical Systems with Two Switches
Guilherme Tavares da Silva, Ricardo Miranda Martins
One of the most common hypotheses on the theory of non-smooth dynamical systems is a regular surface as switching manifold, at which case there is at least well-defined and establi…
A note on Vishik's normal form
Matheus M. Castro, Ricardo M. Martins, Douglas D. Novaes
The Vishik's Normal Form provides a local smooth conjugation with a linear vector field for smooth vector fields near contacts with a manifold. In the present study, we focus on th…