Rotation numbers for quasiperiodically forced circle maps - Mode-locking vs strict monotonicity

Details Rotation numbers for quasiperiodically forced circle maps - Mode-locking vs strict monotonicity Rotation numbers for quasiperiodically forced circle maps - Mode-locking vs strict monotonicity

2006-07-24

arxiv.org/abs/math/0607598v1

Mathematics

Dynamical Systems

12 pages

Scientific paper

We describe the relation between the dynamical properties of a quasiperiodically forced orientation-preserving circle homeomorphism and the behavior of the fibered rotation number with respect to strictly monotone perturbations. Despite the fact that the dynamics in the forced case can be considerably more complicated, the result we obtain is in perfect analogy with the one-dimensional situation. In particular, the fibered rotation number behaves strictly monotonically whenever the rotation vector is irrational. This answers a question posed by Herman (1983, Comm. Math. Helv.).

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