Orbital stability and Zhukovskiǐ quasi-stability in impulsive dynamical systems

In this article, we deal with orbital stability and Zhukovskiǐ quasi-stability of periodic or recurrent orbits in an impulsive dynamical system defined in the n-dimensional Euclidean space Rn{{\mathbb{R}}}^{n}. We show that for a periodic orbit of an impulsive system, its asymptotically orbital stability is equivalent to the asymptotically Zhukovskiǐ quasi-stability, and for a recurrent orbit, the orbital stability is equivalent to the Zhukovskiǐ quasi-stability.