The Lyapunov exponent and the nature of the spectrum:

The nature of the spectrum of  crucially depends on the value of the parameter

So again the distance separating nearest neighboring bands will play a crucial role.

The Lyapunov exponent:




Formulae (3) and (4) show that the Lyapunov exponent becomes "abnormally small" on
the interval  when it becomes close to one of the points