%0 Journal Article
%T Diagonal changes for every interval exchange transformation
%+ Instituto Nacional de Matemática Pura e Aplicada (IMPA)
%+ Institut de Mathématiques de Marseille (I2M)
%A Ferenczi, Sébastien
%< avec comité de lecture
%@ 0046-5755
%J Geometriae Dedicata
%I Springer Verlag
%8 2015
%D 2015
%R 10.1007/s10711-014-0031-y
%Z 37E05; 37B10
%Z Mathematics [math]Journal articles
%X We give a geometric version of the induction algorithms defined in [10] and generalizing the self-dual induction of [17]. For all interval exchanges, whatever the permutation and the disposition of the discontinuities, we define diagonal changes which generalize those of [7]: they are exchange of unions of triangles on a set of triangulated polygons, which may be glued to cre- ate a translation surface. There are many possible algorithms depending on decisions at each step, and when the decision is fixed each diagonal change is a natural extension of the corresponding induction, which extends the result shown in [7] in the particular case of the hyperelliptic Rauzy class. Furthermore, for that class, we can define decisions such that we get an algorithm of diagonal changes which is a natural extension of the underlying algorithm of self-dual induction, and we can thus compute an invariant measure for the normalized induction. The diagonal changes allow us also to realize the self-duality of the induction in the hyperelliptic class, and to prove this does not hold outside that class.
%G English
%2 https://hal.science/hal-01263121/document
%2 https://hal.science/hal-01263121/file/fieaif.pdf
%L hal-01263121
%U https://hal.science/hal-01263121
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ ANR