Abstract
Let Y be a local dendrite with the number of branch points being finite and f:Y→Y be continuous. Denote by P(f), R(f), Ω(f) and ω(x,f) the set of periodic points of f, the set of recurrent points of f, the set of non-wandering points of f and the set of ω-limit points of x under f, respectively. Write ω(f)=∪x∈Yω(x,f) and ωn+1(f)=∪x∈ωn(f)ω(x,f) and Ωn+1(f)=Ω(f|Ωn(f)) for any positive integer n. In this paper, we show that Ω3(f)=R(f)‾ and the depth of f is at most 3, and ω3(f)=ω2(f). Furthermore, we show that R(f)‾=R(f)∪P(f)‾.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
