Common Limits of Fibonacci Circle Maps

Abstract

We show that limits for the critical exponent tending to \infty exist in both critical circle homeomorphisms of golden mean rotation number and Fibonacci circle coverings. Moreover, they are the same. The limit map is not analytic at the critical point, which is flat, but has non-trivial complex dynamics.

to appear in Commun. Math. Phys. arXiv admin note: substantial text overlap with arXiv:math/0306033

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