MOTION TYPES AND CHAOS OF MULTI-BODY SYSTEMS VIBRATING WITH IMPACTS

<正> In this paper,the limit sets theory for an autonomous dynamical system is generalized to amulti-body system vibrating with impacts.We discover that if every motion of the system is bounded,it hasonly four different types:periodic motion 7 t,non-periodic recurrent motion γ2,and non-Poisson stable mo-tions γ3 and γ4 approaching γ1 and γ2, respectively.γ2 is the source of chaos.It is very interesting that cha-otic motions seem stochastic but possess the character of recurrence.By way of example,we discuss chaoticmotions of a small ball bouncing vertically on a massive vibrating table.The result obtained by us is differentfrom that obtained by Holmes.