Working on strongly irreducible planar self-affine sets satisfying the strong open set condition, we calculate the Birkhoff spectrum of continuous potentials and the Lyapunov spectrum.
Bárány, B., Jordan, T., Käenmäki, A., & Rams, M. (2020). Birkhoff and Lyapunov spectra on planar self-affine sets. International Mathematics Research Notices, [rnz359]. https://doi.org/10.1093/imrn/rnz359