In this paper, we classify the global phase portraits of all quadratic planar systems with two parallel invariant straight lines. The main techniques used are Poincaŕe Compactification and Normal Forms Theory combined with ...

The main result of this work is the Poincaré - Bendixson Theorem for planar piecewise smooth vector fields, which tell us what kind of limit sets arise in this context. We will also study details about the concepts of ...

We study the stability of an invisible fold-fold singularity of planar piecewise smooth Hamiltonian vector fields by computing some kind of Lyapunov coefficients. We obtain the general expressions for the first five Lyapunov ...

A large number of papers deal with “Closing Lemmas” for Cr-vector fields (and Cr-diffeomorphisms). Here, we introduce this subject and formalize the terminology about nontrivially recurrent points and nonwandering points ...

In this dissertation, we present results on the existence of limit cycles in planar differential systems, configuration of such cycles and the dynamics of nonlinear systems near periodic orbits.

In this work, we are interested in isolated crossing periodic orbits in planar piecewise polynomial vector fields defined in two zones separated by a straight line. In particular, in the number of limit cycles of small ...

In this paper some aspects on chaotic behavior and minimality in planar piecewise smooth vector fields theory are treated. The occurrence of non-deterministic chaos is observed and the concept of orientable minimality is ...

In this paper some qualitative and geometric aspects of nonsmooth vector felds theory are discussed. A Poincaré-Bendixson Theorem for a class of nonsmooth systems is presented. In addition, a minimal set in planar Filippov ...

It is shown that a spin-1/2 fermion coupled to the axially symmetric electromagnetic vector potential has the same matrix structure as that one for the planar Dirac oscillator. In particular, the planar Dirac oscillator ...