Abstract
Let [Formula: see text] and [Formula: see text] an integer. We consider the collection [Formula: see text] of homogeneous self-similar sets on the line such that every two of copies [Formula: see text] of the self-similar set [Formula: see text] are either separated or overlapped with rank [Formula: see text] in [Formula: see text]. For [Formula: see text] generated by [Formula: see text] similitudes, we denote by [Formula: see text] the number of overlaps with rank [Formula: see text]. The set of points in the self-similar set having a unique coding is called the univoque set and denoted by [Formula: see text]. In this paper, we investigate a uniform method to calculate the Hausdorff dimension of the set [Formula: see text].
Sign-in/Register to access full text options 
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.
