Quasimorphismes sur le monoïde libre, et substitutions dans les mesures invariantes  [ Quasimorphisms on the free monoid, and substitutions in invariant measures ]
Annales de l'Institut Fourier, Volume 67 (2017) no. 6, p. 2651-2678

It will be shown how a morphism σ:A ☆ →B ☆ between two finitely generated free monoids can transform an invariant mesure on A ℕ into an invariant measure on B ℕ . 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.

On montre comment un morphisme σ:A ☆ →B ☆ entre deux monoïdes libres de type fini peut transformer une mesure invariante sur A ℕ en une mesure invariante sur B ℕ . 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.

Received : 2013-04-10
Revised : 2015-08-17
Accepted : 2016-12-06
Published online : 2017-12-14
DOI : https://doi.org/10.5802/aif.3146
Classification:  20M50,  37B10
Keywords: quasimorphism, substitution, rearrangement norm 
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {67},
     number = {6},
     year = {2017},
     pages = {2651-2678},
     doi = {10.5802/aif.3146},
     language = {fr},
     url = {http://www.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, Volume 67 (2017) no. 6, pp. 2651-2678. doi : 10.5802/aif.3146. http://www.numdam.org/item/AIF_2017__67_6_2651_0/

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