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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

Metric properties of boundary maps: Hilbert entropy and non-differentiability

Résumé

We interpret the Hilbert entropy of a convex projective structure on a closed surface of higher genus as the Hausdorff dimension of the non-differentiability points of the limit set in the full flag space F(R^3). Generalizations for regularity properties of boundary maps between locally conformal representations are also discussed. An ingredient for the proofs is the concept of hyperplane conicality that we introduce for a θ-Anosov representation into a reductive real-algebraic Lie group G. In contrast with directional conicality, hyperplane-conical points always have full mass for the corresponding Patterson-Sullivan measures.
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Dates et versions

hal-03898485 , version 1 (14-12-2022)
hal-03898485 , version 2 (06-11-2023)

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Beatrice Pozzetti, Andrés Sambarino. Metric properties of boundary maps: Hilbert entropy and non-differentiability. 2023. ⟨hal-03898485v2⟩
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