Exact dimensionality and Ledrappier-Young formula for the Furstenberg measure

Rapaport, Ariel

doi:10.1090/tran/8405

Exact dimensionality and Ledrappier-Young formula for the Furstenberg measure
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Trans. Amer. Math. Soc. 374 (2021), 5225-5268 Request permission

Abstract:

Assuming strong irreducibility and proximality, we prove that the Furstenberg measure, corresponding to a finitely supported measure on the general linear group of a finite dimensional real vector space, is exact dimensional. We also establish a Ledrappier-Young type formula for its dimension. The general strategy of the proof is based on the argument given by Feng for the exact dimensionality of self-affine measures.

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