Anosov representations with Lipschitz limit set Article Swipe

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Mathematics Lipschitz continuity Limit set Pure mathematics Limit (mathematics) Set (abstract data type) Lipschitz domain Discrete mathematics Mathematical analysis Computer science Programming language

Maria Beatrice Pozzetti , Andrés Sambarino , Anna Wienhard ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.2140/gt.2023.27.3303 · OA: W2980825893

We study Anosov representations whose limit set has intermediate regularity,\nnamely is a Lipschitz submanifold of a flag manifold. We introduce an explicit\nlinear functional, the unstable Jacobian, whose orbit growth rate is integral\non this class of representations. We prove that many interesting higher rank\nrepresentations, including $\\Theta$-positive representations, belong to this\nclass, and establish several applications to rigidity results on the orbit\ngrowth rate in the symmetric space.\n