Dimension maximizing measures for self-affine systems

Abstract

In this paper we study the dimension theory of planar self-affine sets satisfying dominated splitting in the linear parts and strong separation condition. The main results of this paper is the existence of dimension maximizing Gibbs measures (Käenmäki measures). To prove this phenomena, we show that the Ledrappier-Young formula holds for Gibbs measures and we introduce a transversality type condition for the strong-stable directions on the projective space.

The previous version of the paper has been withdrawn by the author due to a crucial error. It was in the previous version in Section 4, Lemma 4.6 equation (4.4). This error annihilated Theorem 1.2