For the same Teichmüller curves with prior degenerate spectra, the non-Abelian analogue has no zero Lyapunov exponents.
Athreya and Howard Masur, Translation surfaces, Graduate Studies in Mathematics, vol
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Infinitesimal random dynamics of certain Veech groups on SU(2)-character varieties
For the same Teichmüller curves with prior degenerate spectra, the non-Abelian analogue has no zero Lyapunov exponents.