78 citations · 155 across the 14 of their papers we have counts for
17 papers
On local minimality of Hausdorff dimension for round limit sets
Sami Douba, Andrés Sambarino, Franco Vargas Pallete
We address a question of Canary--Taylor and Canary--Minsky--Taylor for sufficiently symmetric compact hyperbolic -orbifolds with totally geodesic boundary. We give sufficient co…
Bending, entropy and proper affine actions of surface groups
Martin Bridgeman, Richard Canary, Andres Sambarino
We show that for any closed surface there is an explict neighborhood of the fuchsian locus in quasifuchsian space such that for every representation $ρ\in…
Asymptotic properties of infinitesimal characters and applications
Andrés Sambarino
Inspired by Benoist, we study objects linked to integrable tangent vectors on the character variety of a semi-group with values in a semi-simple real-algebraic group $\mathsf G…
Metric properties of boundary maps, Hilbert entropy and non-differentiability
Beatrice Pozzetti, Andrés Sambarino
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 i…
A report on an ergodic dichotomy
Andrés Sambarino
We establish (some directions) of a Ledrappier correspondence between Hölder cocycles, Patterson-Sullivan measures, etc for word-hyperbolic groups with metric-Anosov Mineyev flow.…
Infinitesimal Zariski closures of positive representations
Andrés Sambarino
We classify the (semi-simple parts of the) Lie algebra of the Zariski closure of a discrete subgroup of a split simple real-algebraic Lie group, whose limit sets are minimal and su…
Hessian of Hausdorff dimension on purely imaginary directions
Martin Bridgeman, Beatrice Pozzetti, Andrés Sambarino +1
We extend classical results of Bridgeman-Taylor and McMullen on the Hessian of the Hausdorff dimension on quasi-Fuchsian space to the class of (1,1,2)-hyperconvex representations,…
Anosov representations with Lipschitz limit set
Beatrice Pozzetti, Andrés Sambarino, Anna Wienhard
We study Anosov representations whose limit set has intermediate regularity, namely is a Lipschitz submanifold of a flag manifold. We introduce an explicit linear functional, the u…
Conformality for a robust class of non-conformal attractors
Beatrice Pozzetti, Andrés Sambarino, Anna Wienhard
In this paper we investigate the Hausdorff dimension of limit sets of Anosov representations. In this context we revisit and extend the framework of hyperconvex representations and…
Simple root flows for Hitchin representations
Martin Bridgeman, Richard Canary, François Labourie +1
We study simple root flows and Liouville currents for Hitchin representations. We show that the Liouville current is associated to the measure of maximal entropy for a simple root…
Anosov representations and dominated splittings
Jairo Bochi, Rafael Potrie, Andrés Sambarino
We provide a link between Anosov representations introduced by Labourie and dominated splitting of linear cocycles. This allows us to obtain equivalent characterizations for Anosov…
Eigenvalues and Entropy of a Hitchin representation
Rafael Potrie, Andrés Sambarino
We show that the critical exponent of a representation in the Hitchin component of is bounded above, the least upper bound being attained only in the Fuchsian l…
On entropy, regularity and rigidity for convex representations of hyperbolic manifolds
Andrés Sambarino
Given a convex representation of a convex co-compact group of we find upper bounds for the quantity where is the…
The pressure metric for Anosov representations
Martin Bridgeman, Richard Canary, Francois Labourie +1
Using the thermodynamics formalism, we introduce a notion of intersection for projective Anosov representations, show analyticity results for the intersection and the entropy, and…
The orbital counting problem for hyperconvex representations
Andres Sambarino
We give a precise counting result on the symmetric space of a noncompact real algebraic semisimple group for a class of discrete subgroups of that contains, for example, r…
Hyperconvex representations and exponential growth
Andres Sambarino
Let be a real algebraic semi-simple Lie group and be the fundamental group of a compact negatively curved manifold. In this article we study the limit cone, introduced by B…
Quantitative properties of convex representations
Andrés Sambarino
Let be a discrete subgroup of and fix some euclidean norm on Let be the number of elements in whose operator norm is $\leq t.…