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We investigate here the properties of substitutive dendric words and prove some rigidity properties, that is, algebraic properties on the set of substitutions that fix a dendric word. We also prove that aperiodic minimal dendric subshifts (generated by dendric words) cannot have rational topological eigenvalues, and thus, cannot be generated by constant length substitutions.<\/jats:p>","DOI":"10.1142\/s0129054118420017","type":"journal-article","created":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T10:47:08Z","timestamp":1534848428000},"page":"705-720","source":"Crossref","is-referenced-by-count":14,"title":["Rigidity and Substitutive Dendric Words"],"prefix":"10.1142","volume":"29","author":[{"given":"V.","family":"Berth\u00e9","sequence":"first","affiliation":[{"name":"IRIF, CNRS UMR 8243, Universit\u00e9 Paris Diderot \u2013 Paris 7, Case 7014, 75205 Paris Cedex 13, France"}]},{"given":"F.","family":"Dolce","sequence":"additional","affiliation":[{"name":"LaCIM, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, 201, Pr\u00e9sident-Kennedy, H2X 3Y7 Montr\u00e9al (Qu\u00e9bec), Canada"}]},{"given":"F.","family":"Durand","sequence":"additional","affiliation":[{"name":"LAMFA, UMR CNRS 7352, Universit\u00e9 de Picardie Jules Verne, 33, rue Saint-Leu, 80039 Amiens Cedex 1, France"}]},{"given":"J.","family":"Leroy","sequence":"additional","affiliation":[{"name":"D\u00e9partement de Math\u00e9matiques, Universit\u00e9 de Li\u00e8ge, 12, All\u00e9e de la D\u00e9couverte, 4000 Li\u00e8ge, Belgium"}]},{"given":"D.","family":"Perrin","sequence":"additional","affiliation":[{"name":"LIGM, UMR CNRS 8049, Universit\u00e9 Paris-Est Marne-la-Vall\u00e9e, 5, bd Descartes, Champs sur Marne 77454 Marne-la-Vall\u00e9 Cedex 2, France"}]}],"member":"219","published-online":{"date-parts":[[2018,8,21]]},"reference":[{"key":"S0129054118420017BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2012.07.020"},{"key":"S0129054118420017BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2012.07.013"},{"key":"S0129054118420017BIB003","first-page":"81","volume":"46","author":"Berth\u00e9 V.","year":"2014","journal-title":"RIMS Lecture note \u2018Kokyuroku Bessatu\u2019"},{"key":"S0129054118420017BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2012.01.001"},{"key":"S0129054118420017BIB005","doi-asserted-by":"publisher","DOI":"10.4064\/aa122-4-1"},{"key":"S0129054118420017BIB006","doi-asserted-by":"publisher","DOI":"10.1051\/ita:2007026"},{"key":"S0129054118420017BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00605-014-0721-4"},{"key":"S0129054118420017BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2014.12.010"},{"key":"S0129054118420017BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2014.09.014"},{"key":"S0129054118420017BIB010","doi-asserted-by":"publisher","DOI":"10.5802\/aif.2403"},{"key":"S0129054118420017BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/BF00534241"},{"key":"S0129054118420017BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2009.01.022"},{"key":"S0129054118420017BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2016.01.008"},{"key":"S0129054118420017BIB015","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/385\/07188"},{"key":"S0129054118420017BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(97)00029-0"},{"key":"S0129054118420017BIB018","doi-asserted-by":"crossref","first-page":"1799","DOI":"10.4171\/jems\/294","volume":"13","author":"Durand F.","year":"2011","journal-title":"J. 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