In this paper,the limit sets theory for an autonomous dynamical system is generalized to a multi-body system vibrating with impacts.We discover that if every motion of the system is bounded,it has only four different ...In this paper,the limit sets theory for an autonomous dynamical system is generalized to a multi-body system vibrating with impacts.We discover that if every motion of the system is bounded,it has only 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 chaotic motions of a small ball bouncing vertically on a massive vibrating table.The result obtained by us is different from that obtained by Holmes.展开更多
基金The project supported by National Natural Science Foundation of China
文摘In this paper,the limit sets theory for an autonomous dynamical system is generalized to a multi-body system vibrating with impacts.We discover that if every motion of the system is bounded,it has only 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 chaotic motions of a small ball bouncing vertically on a massive vibrating table.The result obtained by us is different from that obtained by Holmes.
