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Limit cycles from a monodromic infinity in planar piecewise linear systems. (English) Zbl 1477.34059

Planar piecewise linear systems separated by a straight line have been extensively studied. Here, there are adopted some new techniques via changes of variables and parameters, a reduced canonical form with five parameters is obtained. Then a more direct approach is introduced to characterize the stability and bifurcations of the periodic orbit at infinity. The authors show that the Hopf bifurcation at infinity can have degeneracies of co-dimension three and, in particular, up to three limit cycles can bifurcate from the periodic orbit at infinity.

MSC:

34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
34A36 Discontinuous ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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