Eigenvalues and simplicity of interval exchange transformations
Résumé
For a class of d-interval exchange transformations, whichwe call the symmetric class,
we deÞne a new self-dual induction process in which the system is successively induced on a union of
sub-intervals. This algorithm gives rise to an underlying graph structure which reßects the dynamical
behavior of the system, through theRokhlin towers of the induced maps. We apply it to build a wide as-
sortment of explicit examples on four intervals having different dynamical properties: these include the
Þrst nontrivial examples with eigenvalues (rational or irrational), the Þrst ever example of an exchange
on more than three intervals satisfying VeechÕs simplicity (though this weakening of the notion of min-
imal self-joinings was designed in 1982 to be satisÞed by interval exchange transformations), and an
unexpected example which is non uniquely ergodic, weakly mixing for one invariant ergodic measure
but has rational eigenvalues for the other invariant ergodic measure.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)
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