拓扑熵为+∞的系统与拓扑熵映侵的连续性

摘要

A system has been constructed in this paper, the topologi calentropy is + ∞, and proved topological entropy mapping ent(f) is continuous on topologic al space:Γ={f|f∈C0,f:I→I nonvariable, f with constant slope λ>1,λ∈R+}Which is lead by the uniform convergence. And exist nonenumerable mapping setΓ0Γ,f∈Γ0,ent(f)=+∞.%文章构造一个拓扑熵为+∞的系统,证明了拓扑熵映射ent(f)在一致收敛诱导的拓扑空间:Γ={f|f∈C0(I),f:I→I不变,f有常斜率λ>1;λ∈R+}上是连续的,且存在不可数映射集合Γ0Γ,f∈Γ0,有ent(f)=+∞。