Separated families of Anosov representations have critical exponents asymptotic to a combinatorial invariant computable from finite graph spectral data, yielding bounds on the Thurston asymmetric metric and analysis of convex projective degenerations on a pair of pants.
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Asymptotics are established for counting orbital points lying in one conjugacy class for cocompact and convex cocompact actions on negatively curved spaces.
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On separated families of Anosov representations
Separated families of Anosov representations have critical exponents asymptotic to a combinatorial invariant computable from finite graph spectral data, yielding bounds on the Thurston asymmetric metric and analysis of convex projective degenerations on a pair of pants.
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Orbital Counting in Conjugacy Classes
Asymptotics are established for counting orbital points lying in one conjugacy class for cocompact and convex cocompact actions on negatively curved spaces.