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# Necessary condition for the basin of attraction of a periodic orbit in non-smooth periodic systems

• We study a time-periodic non-smooth differential equation $\dot{x}=f(t,x)$, $x\in \mathbb R$. In [4] we have presented a sufficient condition for existence, uniqueness, stability and the basin of attraction of a periodic orbit in such a system, which is a generalized Borg's condition. In this paper we prove that this condition is necessary. The proof involves a generalization of Floquet exponents for periodic orbits of non-smooth differential equations.
Mathematics Subject Classification: 34C25, 34A36.

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