摘要
研究拓扑动力系统(X,f)的拓扑熵ent^*(f)和它诱导的超空间拓扑动力系统(K(X),f^-)拓扑熵ent^*(f)之间的关系。利用拓扑熵ent^*(f)的性质,以拓扑动力系统与它诱导的超空间拓扑动力系统之间的关系为切入点。得出了拓扑动力系统(X,f)的拓扑熵不大于它诱导的超空间拓扑动力系统(K(X),f^-)的拓扑熵;当拓扑动力系统(X,f)的拓扑熵大于0时,超空间拓扑动力系统(K(X),f^-)的拓扑熵为∞。ent^*(f)具有Adler拓扑熵和Bowen拓扑熵的一般性质。
To study the connection between topological entropy ent^*(f) of dynamical system (X,f) and topological entropy ent^*(f) of induced hyperspace dynamical system (K(X), f^-). Use the properties of topological entropy ent^*(f) as well as the relationship between the two dynamics. Two results were obtained. (1) ent^8(f^-)≤ent^*(f^-).(2)If the base map has positive topological entropy, corresponding hyperspace map has infinite topological entropy. The topological entropy ent^*(f) has the general properties as topological entropy defined by Adler and Bowen.
基金
陕西省自然科学基金资助项目(SJ08A24)