Let I be a compact real interval and let f:I → I be continuous. We describe an interval analogy of the irrational circle rotation that occurs as a subsystem of the dynamical system (I,f)-we call it an irrational twist system. Using a coding we show that any irrational twist system is strictly ergodic. We also prove that irrational twist systems exist as subsystems of a large class of systems (I,f) having a cycle of odd period greater than one.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-2-1,
author = {Jozef Bobok},
title = {Twist systems on the interval},
journal = {Fundamenta Mathematicae},
volume = {173},
year = {2002},
pages = {97-117},
zbl = {1082.37036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-2-1}
}
Jozef Bobok. Twist systems on the interval. Fundamenta Mathematicae, Tome 173 (2002) pp. 97-117. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm175-2-1/