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arXiv · 1104.3762

Absorbing sets of homogeneous subtractive algorithms

Tomasz Miernowski·Arnaldo Nogueira
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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.

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Tomasz Miernowski, Arnaldo Nogueira. 2011-04-19. Absorbing sets of homogeneous subtractive algorithms. https://arxiv.org/abs/1104.3762

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