{"title":"Modulus of continuity for spectral measures of suspension flows over Salem type substitutions","authors":"Juan Marshall-Maldonado","doi":"10.1007/s11856-024-2630-0","DOIUrl":null,"url":null,"abstract":"<p>We study the spectrum of the self-similar suspension flows of subshifts arising from primitive substitutions. We focus on the case where the substitution matrix has a Salem number <i>α</i> as dominant eigenvalue. We obtain a Hölder exponent for the spectral measures for points away from zero and belonging to the field ℚ(<i>α</i>). This exponent depends only on three parameters of each of these points: its absolute value, the absolute value of its real conjugate and its denominator.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11856-024-2630-0","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We study the spectrum of the self-similar suspension flows of subshifts arising from primitive substitutions. We focus on the case where the substitution matrix has a Salem number α as dominant eigenvalue. We obtain a Hölder exponent for the spectral measures for points away from zero and belonging to the field ℚ(α). This exponent depends only on three parameters of each of these points: its absolute value, the absolute value of its real conjugate and its denominator.
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