# American Institute of Mathematical Sciences

February & March  2007, 18(2&3): 355-373. doi: 10.3934/dcds.2007.18.355

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

 1 Zentrum Mathematik, TU München, Boltzmannstr. 3, D-85747 Garching bei München

Received  March 2006 Revised  July 2006 Published  March 2007

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.
Citation: Peter Giesl. Necessary condition for the basin of attraction of a periodic orbit in non-smooth periodic systems. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 355-373. doi: 10.3934/dcds.2007.18.355
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