Infinitesimal random dynamics of certain Veech groups on SU(2)-character varieties

TL;DR

This paper investigates the Lyapunov spectrum of non-Abelian analogues of certain SL(2,R)-invariant subbundles over Teichmüller curves, showing they have no zero exponents, extending previous findings on Abelian cases.

Contribution

It demonstrates that the non-Abelian analogues of previously studied invariant subbundles have no zero Lyapunov exponents, revealing new dynamical properties.

Findings

Non-Abelian analogues have no zero Lyapunov exponents.

Extends previous results on Abelian cases to non-Abelian settings.

Provides insights into the dynamics of Veech groups on SU(2)-character varieties.

Abstract

Almost 20 years ago, the first and fourth authors found examples of SL(2,R)-invariant subbundles of Hodge bundles over Teichm\"uller curves having maximally degenerate Lyapunov spectrum. For these same surfaces, we show that a natural non-Abelian analogue has no zero Lyapunov exponents.