Uniqueness of the measure with full dimension on sofic affine-invariant subsets of the 2-torus

摘要

We consider the variational principle for dimension on compact subsets of the 2-torus which are invariant under a non-conformal expanding diagonal endomorphism. Condition (H) ensures that the invariant measures with full dimension are the equilibrium states of some potential function. This result applies to the problem of uniqueness of the measure with full dimension on the sofic affine-invariant sets.