L^q-spectra of measures on non-conformal attractors
Ergodic Theory and Dynamical Systems Seminar
6th May 2021, 2:00 pm – 3:00 pm
Online, on zoom (if interested, please email one of the organisers to gain access to the Zoom link),
We study Bernoulli measures in the plane supported on sets defined by iterated function systems consisting of nonlinear, non-conformal maps. These maps have triangular Jacobian matrices and satisfy an appropriate separation condition. Using ideas from thermodynamic formalism we are able to calculate the L^q-spectrum of such measures and as a corollary we obtain the box dimension of the sets they are supported on. This is joint work with Kenneth Falconer and Jonathan Fraser.