Work

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

Year: 2026

Type: article

Abstract: We interpret the Hilbert entropy of a convex projective structure on a closed higher-genus surface 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 measure.

Source: Annales Henri Lebesgue

DOI: 10.5802/ahl.265

Authors: Maria Beatrice Pozzetti, Andrés Sambarino

Institutions: University of Bologna, Centre National de la Recherche Scientifique, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Deutsche Forschungsgemeinschaft, Agence Nationale de la Recherche