Abstract
Let f :G→G be a strictly piecewise monotone continuous map on a finite graph G . By investigating the topological structure of the inverse limit space (G,f) using f as a sole bonding map, we show that the following statements are equivalent: (1) (G,f) contains no indecomposable subcontinuum. (2) The topological entropy of f is zero. (3) (G,f) is Suslinean. (4) Each homeomorphism of (G,f) has zero topological entropy. (5) f has finitely many nontrivial minimal sets. (6) The set of recurrent points of f is closed. (7) Each ω -limit point is a recurrent one. (8) Each recurrent point of f is an almost periodic one.
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.
