This survey article is concerned with the study of bifurcations of discontinuous piecewise-
smooth maps, with a special focus on the one-dimensional case. We review the literature on …

In this paper periodic trajectories of dynamical systems presenting discontinuities are
studied. The considered model consists of two distinct linear differential systems, each one …

The first author is supported by Ministerio de Economía y Competitividad through the project
MTM2015-65608-P and by Junta de Andaucía by project P12-FQM-1658. The second …

Consider a piecewise linear dynamical system in ℝ 3, divided by a switching plane, with the
Teixeira Singularity (TS). Under the antiparallelism hypothesis, it is known that the system …

Apart from being a complex task even in piecewise linear systems, the proof of the existence
of homoclinic connections and T–point heteroclinic cycles must be usually carried out in …

In this paper we present a number of results involving 3D nonsmooth dynamical systems
tangent to a foliation. We study one-parameter families of systems Z ε passing through a …

The main goal of this work is to describe the periodic behavior of a class of three-
dimensional reversible piecewise linear continuous systems. More concretely, we study an …

The geometries related to the bifurcation and chaos of a partial differential equation
describing the unsteady combustion of solid propellants are investigated. Under the …

In a previous talk by F. Fernández-Sánchez, a piecewise linear version of Michelson system
[5], x= y, y= z, z= 1-y-λ (1+ λ2)| x|, with λ> 0,(1) was presented, together with the analysis of …

Applying new results from the averaging theory for continuous and discontinuous differential
systems, we study the periodic solutions of two distinct versions of the Michelson differential …