Title: Dimensions of equilibrium measures on a class of planar self-affine sets,
Abstract: 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 explicit expression for
the dimension in terms of the entropy and Lyapunov exponents as well as the
dimension of the important coordinate projection of the measure. In particular,
we do this by showing that the Käenmäki measure is equal to the sum of (the
pushforwards) of two Gibbs measures on an associated subshift of finite type.