Dimension maximizing measures for self-affine systems

Bárány, Balázs; Rams, Michał

doi:10.1090/tran/7103

Dimension maximizing measures for self-affine systems

Authors: Balázs Bárány and Michał Rams
Journal: Trans. Amer. Math. Soc. 370 (2018), 553-576
MSC (2010): Primary 28A80; Secondary 37C45
DOI: https://doi.org/10.1090/tran/7103
Published electronically: July 7, 2017
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Abstract: In this paper we study the dimension theory of planar self-affine sets satisfying dominated splitting in the linear parts and the strong separation condition. The main result 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.

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