Limit cycles of 3-dimensional discontinuous piecewise differential systems formed by linear centers
Copyright policy )Limit cycles of 3-dimensional discontinuous piecewise differential systems formed by linear centers
In this paper we deal with 3-dimensional discontinuous piecewise differential systems formed by linear centers and separated by one plane or two parallel planes. We prove that these systems separated by one plane have no limit cycles, besides the systems separated by two parallel planes have at most one limit cycle, and that there are systems having such a limit cycle. So we solve the extension of the 16th Hilbert problem to this class of differential systems.
Bifurcation theory for ordinary differential equations, limit cycles, discontinuous piecewise differential systems, linear centers, first integrals, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Discontinuous ordinary differential equations, periodic orbits, Limit cycles, First integrals, Explicit solutions, first integrals of ordinary differential equations, Discontinuous piecewise differential systems, Periodic orbits, Linear centers
Bifurcation theory for ordinary differential equations, limit cycles, discontinuous piecewise differential systems, linear centers, first integrals, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Discontinuous ordinary differential equations, periodic orbits, Limit cycles, First integrals, Explicit solutions, first integrals of ordinary differential equations, Discontinuous piecewise differential systems, Periodic orbits, Linear centers
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