Dimension maximizing measures for self-affine systems

Balázs Bárány; Michał Rams

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arXiv · 1507.02829

Dimension maximizing measures for self-affine systems

Balázs Bárány·Michał Rams

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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 strong separation condition. The main results of this paper is the existence of dimension maximizing Gibbs measures (K\"aenm\"aki 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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Balázs Bárány, Michał Rams. 2015-07-10. Dimension maximizing measures for self-affine systems. https://arxiv.org/abs/1507.02829

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