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.
No takes yet. Share an insight, caveat, or question.
Éric Olivier (2009) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: