Computation of rotation numbers  for a class of PL-circle homeomorphisms

Abdelhamid Adouani; Habib Marzougui

doi:10.3934/dcds.2012.32.3399

Article Contents

2012, Volume 32, Issue 10: 3399-3419. Doi: 10.3934/dcds.2012.32.3399

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Computation of rotation numbers for a class of PL-circle homeomorphisms

Abdelhamid Adouani^1, and
Habib Marzougui^1,

1.
University of Carthage, Faculty of Science of Bizerte, Department of Mathematics, Zarzouna, 7021

Received: April 30, 2011

Revised: January 31, 2012

Published: September 2012

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Abstract

We give an explicite formula to compute rotation numbers of piecewise linear (PL) circle homeomorphisms $f$ with the product of $f$-jumps in the break points contained in a same orbit is trivial. In particular, a simple formulas are then given for particular PL-homeomorphisms such as the PL-Herman's examples. We also deduce that if the slopes of $f$ are integral powers of an integer $m\geq 2$ and break points and their images under $f$ are $m$-adic rational numbers, then the rotation number of $f$ is rational.

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Mathematics Subject Classification: Primary: 37C15, 37E10, 37E45.

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References

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