中文摘要：

针对非光滑动力学系统特点，在胞映射思想基础上，引入拉回积分等分析手段，得到了非光滑系统吸引子和吸引域的胞映射计算方法．并以一类碰振系统为例，给出了其吸引子和具有复杂分形边界的吸引域，并验证了该方法的有效性．

英文摘要：

In view of the characteristics of non-smooth dynamical systems, the pullback integral method is introduced into the impact process based on the cell-mapping method. The method for calculating the attractors and domains of attraction of non-smooth dynamical systems is investigated. Through the analysis of a nonlinear dynamical system with rigid constraints, coexistent attractors and domains of attraction with complicated fractal boundary are obtained. Compared with the phase portraits,the present results are validated to be reasonable.