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Article Dans Une Revue Monatshefte für Mathematik Année : 2012

Absorbing sets of homogeneous subtractive algorithms

Arnaldo Nogueira
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Résumé

We 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.

Dates et versions

hal-01268436 , version 1 (04-02-2016)

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Arnaldo Nogueira. Absorbing sets of homogeneous subtractive algorithms. Monatshefte für Mathematik, 2012, 167, pp.547-569. ⟨10.1007/s00605-012-0385-x⟩. ⟨hal-01268436⟩
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