Absorbing sets of homogeneous subtractive algorithms

International audienceWe consider homogeneous multidimensional continued fraction algo- rithms, 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 con- jecture due to Schweiger. Other homogeneous algorithms are also analysed including ones which are ergodic