On separated families of Anosov representations
Geometric Topology
2026-05-15 v2 Dynamical Systems
Abstract
We introduce different notions of separation for families of Anosov representations. We show that, along a diverging sequence of such families, the critical exponent is asymptotic to a combinatorial invariant computable from the spectral data of a finite graph. Our method allows us to derive bounds on the Thurston asymmetric metric. As an application, we study specific degenerations of convex projective structures on a pair of pants, generalizing an example of McMullen.
Keywords
Cite
@article{arxiv.2604.18994,
title = {On separated families of Anosov representations},
author = {Joaquín Lejtreger and Joaquín Lema},
journal= {arXiv preprint arXiv:2604.18994},
year = {2026}
}
Comments
35 pages, 3 figures v2: fixed some references, improved exposition