Rotation numbers in the infinite annulus. (English) Zbl 0990.37029
The paper deals with rotation numbers in the infinite annulus. It is well-known that in the case of a homeomorphism of the open annulus the existence of the rotation number is more complicated. First of all, the existence of a rotation number for a point is not stable by conjugacy. The author presents the notion of free transverse triangulation and using this proves that the rotation number of a given probability measure invariant by a homeomorphism of the open annulus depends continuously on the homeomorphism under some boundedness conditions.
Reviewer: Messoud Efendiev (Berlin)
MSC:
| 37E45 | Rotation numbers and vectors |
| 37E30 | Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces |
| 37A05 | Dynamical aspects of measure-preserving transformations |
References:
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