Abstract
The box dimension (or 'capacity') of a class of self-affine sets in the plane is calculated. The formula for box dimension given here has a similar form to Bowen's formula for the Hausdorff dimension of self-similar sets, involving the topological pressure of certain functions. The sets studied appear in two contexts; as graphs of generalised Weierstrass functions and as repellers in some foliation preserving maps of the cylinder. The author uses the techniques of the 'singularity spectrum' in order to carry out the calculations.
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.
