Abstract
We investigate the dimension theory of inhomogeneous self-affine carpets. Through the work of Olsen, Snigireva and Fraser, the dimension theory of inhomogeneous self-similar sets is now relatively well-understood, however, almost no progress has been made concerning more general non-conformal inhomogeneous attractors. If a dimension is countably stable, then the results are immediate and so we focus on the upper and lower box dimensions and compute these explicitly for large classes of inhomogeneous self-affine carpets. Interestingly, we find that the `expected formula' for the upper box dimension can fail in the self-affine setting and we thus reveal new phenomena, not occurring in the simpler self-similar case.
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.
