Quantitative properties of convex representations

By Andr'es Sambarino. 2011

78 citations recorded by the source corpus.

Letbe a discrete subgroup of PGL.d; R/. Fix a norm kk on R d and letN� .t/ be the number of elements inwhose operator norm ist. In this article we prove an asymptotic for the growth ofN� .t/ whent !1 for a class of� 's which contains, in particular, Hitchin representations of surface groups and groups dividing a convex set of P.R d /. We also prove analogue counting theorems for the growth of the spectral radii. More precise information is given for Hitchin representations.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fca5501e21edb547872ea25f7439f84a64acfff9

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

An invitation to higher Teichm\"uller theory (2018, background): “Other important quantities that have been investigated using this dynamical viewpoint are the critical exponent and the topological entropy of Hitchin representations, which are related to counting orbit points on the symmetric space [99, 98, 94].”
Conformality for a robust class of non-conformal attractors (2019, background): “ace USwith an Anosov ﬂow whose periodic orbits correspond to conjugacy classes of π1S.We will ﬁx such a metric from now on, this is an (irrelevant) auxiliary choice. One has the following result from [49], see also [8, Section 4] for an explicit construction that works for any hyperbolic group. The ”
Hyperconvex representations and exponential growth (2012, background): “e and denote g the g-invariant complement of g + (this is V = g + g ). g + is an attractor on P(V) for the action of gand g is a repelling hyperplane. 3 CONVEX REPRESENTATIONS 13 Lemma 3.2 (x5 of A.S.[20]). Let ˆ: !PGL(V) be a strictly convex representation. Then for every 2 ˆ( ) is proximal, ˘( +) ”
AN INVITATION TO HIGHER TEICHMÜLLER THEORY (2019, unknown): “Andrés Sambarino (2014b).”
Invariant Measures for Horospherical Actions and Anosov Groups (2020, background): “2 in [43] extends to general Anosov subgroups (see also [11, Thm.”
The pressure metric for Anosov representations (2013, unknown): “Corollary 3.3.”
Eigenvalues and entropy of a Hitchin representation (2014, methodology): “The main purpose of this section and Section 4 is to extend several results from [34] and [33] to the Anosov representations setting.”
The orbital counting problem for hyperconvex representations (2012, background): “In Section 2, we recall results on Hölder cocycles from [27], of particular interest is the Reparametrizing Theorem 2.”