The study of piecewise linear differential equations (PWLDE) has been of great interest in the last decades, as they have been proven to be rich in applications. For example, they can predict periodic oscillations in electric circuits. From a purely mathematical point of view, the area has attracted much study as well, for most of the results of the theory of smooth differential equations cannot be applied to the non-smooth case. In this work, we use first integrals (i.e., functions that are only constant on the orbits of a differential equation) to describe the orbits in each smooth portion of the plane. If the switching plane is of the crossing kind, then one can concatenate orbits of the different regions of the space. Using this method we can investigate the existence of periodic orbits and limit cycles in three-dimensional PWLDE with one or two switching planes.

Apoio/Financiamento da Pesquisa: IC Voluntária