| Abstract: |
We consider skew-product maps over circle rotations x→ x+α (mod 1)
with factors that take values in SL(2,R).
In numerical experiments with α the inverse golden mean,
Fibonacci iterates of almost Mathieu maps
with rotation number 1/4 and positive Lyapunov exponent
exhibit asymptotic scaling behavior.
We prove the existence of such asymptotic scaling
for ``periodic'' rotation numbers and for large Lyapunov exponent.
The phenomenon is universal,
in the sense that it holds for open sets of maps,
with the scaling limit being independent of the maps.
The set of maps with a given periodic rotation number
is a real analytic manifold of codimension 1 in a suitable space of maps.
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