Absorbing sets of homogeneous subtractive algorithms
Dynamical Systems
2011-04-20 v1
Abstract
We consider homogeneous multidimensional continued fraction algorithms, in particular a family of maps which was introduced by F. Schweiger. We prove his conjecture regarding the existence of an absorbing set for those maps. We also establish that their renormalisations are nonergodic which disproves another conjecture due to Schweiger. Other homogeneous algorithms are also analysed including ones which are ergodic.
Cite
@article{arxiv.1104.3762,
title = {Absorbing sets of homogeneous subtractive algorithms},
author = {Tomasz Miernowski and Arnaldo Nogueira},
journal= {arXiv preprint arXiv:1104.3762},
year = {2011}
}