Abstract
We analyze and describe the weighted multifractal spectrum of V-statistics. The description will be possible when the condition of “weighted saturation” is fulfilled. This means that the weighted topological entropy of the set of generic points of measure $$\mu $$ equals the measure-theoretic entropy of $$\mu $$ . Zhao et al. (J Dyn Differ Equ 30:937–955, 2018) proved that for any ergodic measure weighted saturation is verified, generalizing a result of Bowen. Here we prove that under a property of “weighted specification” the saturation holds for any measure. From this we obtain the description of the spectrum of V-statistics. This generalizes the variational result that Fan, Schmeling and Wu obtained for the non-weighted case ( arXiv:1206.3214v1 , 2012).
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.
