Strongly Non-wanderingness in Stability Theory

다국어 초록 (Multilingual Abstract)

The abstract theory of dynamical systems have been distinguished various properties such as periodicity, Poisson stability, non-wanderingness, chain recurrence, etc. The weakest property among them is the property of a point to be chain recurrent. It is due to C. Conley [5]. Bronstein and Kopanskii [4]introduced the concepts of weakly non-wandering set and chain recurrent set for dispersive dynamical systems(or a dynamical system without uniqueness) and said that, in general, it remains unknown whether or not the weakly nonwandering set is equal to the chain recurrent set.
In [7], we introduced the concept of weakly nonwandening set and weakly Poisson stable set for a dynamical system (with uniqueness), and showed that he weakly nonowandering set is properly contained in the chain recurrent set. Moreocer, we proved that the nonwandering set is equal to the chain recurrent set if the system f has POTP(pseido-orbit tracing property). On the other hand, we claimed that the concept of weakly Poisson stability is weaker than that of Poisson stability and stronger than that of non-wanderingness. The purpose of this paper is to study the strongly nonwandering sets that is another proper subset of the nonwandering set.