We study a certain class of weakly order preserving, non-invertible circle maps with irrational rotation numbers and exactly one flat interval. For this class of circle maps we explain the geometric and dynamic structure of orbits. In particular, we formulate the so called upper and lower scaling rules which show an asymmetric and double exponential decay of geometry.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-3-4,
author = {Jacek Graczyk},
title = {Dynamics of circle maps with flat spots},
journal = {Fundamenta Mathematicae},
volume = {209},
year = {2010},
pages = {267-290},
zbl = {1209.37048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-3-4}
}
Jacek Graczyk. Dynamics of circle maps with flat spots. Fundamenta Mathematicae, Tome 209 (2010) pp. 267-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm209-3-4/