Abstract: There are plenty of examples of sets, such as planar carpets, whose box and Assouad dimensions are different. The Assouad spectrum is a one parameter family of dimensions which gives additional information about the fine scale geometry of such sets. In the talk, we will present a formula for the Assouad spectrum of Gatzouras-Lalley carpets. We will highlight why it can be expressed as the concave conjugate of an explicit piecewise-analytic function and, among dynamically invariant sets, what novel features does the spectrum exhibit. Based on joint work with A. Banaji, J.M. Fraser and A. Rutar.
Assouad spectrum of planar carpets
12.01.2024 15:30 - 16:30
Organiser:
H. Bruin, R. Zweimüller
Location: