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Periodic orbits in some piecewise differential systems

Abstract

We will study problems related to the existence, nonexistence, and bifurcation of isolated periodic orbits (limit cycles) in planar piecewise polynomial systems. The first problem is the extension of Bendixson Dulac's theory in piecewise differential systems defined in two zones. The second is the simultaneous bifurcation of limit cycles near piecewise Hamiltonian centers with more than one period annulus. The third problem is related to the simultaneous invariant cones in 3D-piecewise differential systems. The last is related to the number of limit cycles in piecewise quadratic Kolmogorov planar systems. (AU)

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