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Proceedings of the London Mathematical Society Advance Access published online on October 8, 2009
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdp037
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© 2009 London Mathematical Society

Affine interval exchange maps with a wandering interval

S. Marmi

Scuola Normale Superiore
Piazza dei Cavalieri 7, 56126 Pisa
Italy

P. Moussa

Institut de Physique Théorique
CEA/Saclay
91191 Gif-Sur-Yvette
France
pierre.moussa@cea.fr

J.-C. Yoccoz

Collège de France
3, Rue d’Ulm
75005
Paris
jean-c.yoccoz@college-de-france.fr

Received 20 June 2008. Revision received 12 March 2009.

For almost all interval exchange maps (i.e.m.) T0, with combinatorics of genus g ≥ 2, we construct affine i.e.m. T that are semi-conjugate to T0 and have a wandering interval.

2000 Mathematics Subject Classification Primary: 37C15 (Topological and differentiable equivalence, conjugacy, invariants, moduli, classification); Secondary: 37E05 (maps of the interval), 11J70 (Continued fractions and generalizations)


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