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On the Bifurcation of Periodic Orbits in Discontinuous Systems

Commun. Math. Anal.
Volume 8, Number 1 (2010), 87 - 108

On the Bifurcation of Periodic Orbits in Discontinuous Systems

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Abstract

We study behaviour of $T$--periodic trajectories in time-perturbed discontinuous systems, that transversally cross the discontinuity boundary. Sufficient condition of Melnikov-type is stated, under which the original piecewise $C^1$-orbit persists. Applications of derived result are also given to discontinuous planar systems

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