Equilibrium measures of the natural extension of beta-shifts
C.-E. Pfister, W.G. Sullivan
TL;DR
This paper characterizes when equilibrium measures for functions with bounded oscillations in the natural extension of beta-shifts are weak Gibbs measures, based on a specific condition on beta.
Contribution
It provides a necessary and sufficient condition on beta for equilibrium measures to be weak Gibbs measures in this context.
Findings
Identifies the precise condition on beta for weak Gibbs property
Establishes a link between beta and equilibrium measures
Advances understanding of measure properties in beta-shifts
Abstract
We give a necessary and sufficient condition on beta of the natural extension of a beta-shift, so that any equilibrium measure for a function of bounded total oscillations is a weak Gibbs measure.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · semigroups and automata theory