Dimensions of equilibrium measures on a class of planar self-affine sets
Dimensions of equilibrium measures on a class of planar self-affine sets
We study equilibrium measures (Käenmäki measures) supported on self-affine sets generated by a finite collection of diagonal and anti-diagonal matrices acting on the plane and satisfying the strong separation property. Our main result is that such measures are exact dimensional and the dimension satisfies the Ledrappier–Young formula, which gives an …