For the same Teichmüller curves with prior degenerate spectra, the non-Abelian analogue has no zero Lyapunov exponents.
Schwarz, The topology of algebraic quotients, Topological methods in algebraic transformation groups (New Brunswick, NJ, 1988), Progr
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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.