Abstract
Let (X,d) be a compact metric space, f:X→X be a continuous transformation with the almost weak specification property and φ:X→R be a continuous function. We consider the set (called the irregular set for φ) of points for which the Birkhoff average of φ does not exist and show that this set is either empty or carries full Bowen upper and lower metric mean dimension.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.