On montre comment un morphisme entre deux monoïdes libres de type fini peut transformer une mesure invariante sur en une mesure invariante sur . L’existence de cette opération est intimement liée à un résultat de représentation des quasimorphismes homogènes sur le monoïde libre. On étudiera ses propriétés, en particulier vis-à-vis de la distance de réarrangement.
It will be shown how a morphism between two finitely generated free monoids can transform an invariant mesure on into an invariant measure on . The existence of this operation is intimately related to a representation result for homogeneous quasimorphisms on the free monoid. Its properties will be studied, in particular with respect to the rearrangement distance.
Révisé le : 2015-08-16
Accepté le : 2016-12-05
Publié le : 2017-12-13
Classification : 20M50, 37B10
Mots clés : quasimorphisme, substitution, norme de réarrangement
@article{AIF_2017__67_6_2651_0, author = {Bousch, Thierry}, title = {Quasimorphismes sur le mono\"\i de libre, et substitutions dans les mesures invariantes}, journal = {Annales de l'Institut Fourier}, pages = {2651--2678}, publisher = {Association des Annales de l'institut Fourier}, volume = {67}, number = {6}, year = {2017}, doi = {10.5802/aif.3146}, language = {fr}, url = {archive.numdam.org/item/AIF_2017__67_6_2651_0/} }
Bousch, Thierry. Quasimorphismes sur le monoïde libre, et substitutions dans les mesures invariantes. Annales de l'Institut Fourier, Tome 67 (2017) no. 6, pp. 2651-2678. doi : 10.5802/aif.3146. http://archive.numdam.org/item/AIF_2017__67_6_2651_0/
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