Abstract
We study images of equilibrium (Gibbs) states for a class of non-invertible transformations associated to conformal iterated function systems (IFSs) with overlaps [Formula: see text]. We prove exact dimensionality for these image measures, and find a dimension formula using their overlap numbers. In particular, we obtain a geometric formula for the dimension of self-conformal measures for IFSs with overlaps, in terms of the overlap numbers. This implies a necessary and sufficient condition for dimension drop. If [Formula: see text] is a self-conformal measure, then [Formula: see text] if and only if the overlap number [Formula: see text]. Examples are also discussed.
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.
