Limit cycles of discontinuous piecewise differential Hamiltonian systems separated by a circle, or a parabola, or a hyperbola

Abstract

Piecewise differential systems in the plane have been extensively studied in the last two decades, due to the vast application of these systems to describe natural phenomena. The knowledge of the existence or not of periodic solutions, in particular, of the limit cycles, is very important for understanding the dynamics of the differential systems. In this article we studied the maximum number of limit cycles of discontinuous piecewise differential systems, formed by two Hamiltonians systems of degree one with three distinct lines of discontinuity either a circle, or a parabola, or a hyperbola