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UID:6131@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220302T103000
DTEND;TZID=Europe/Paris:20220302T120000
DTSTAMP:20241120T200918Z
URL:https://www.i2m.univ-amu.fr/evenements/contribution-to-the-study-of-su
 bstitutive-dynamical-systems/
SUMMARY:Juan Marshall (I2M\, Aix-Marseille Université): Contribution to th
 e study of substitutive dynamical systems
DESCRIPTION:Juan Marshall: This thesis studies the spectrum of systems asso
 ciated to substitutions\, in particular the continuous spectrum. We have b
 ased the analysis on the study of the spectral cocycle and twisted Birkhof
 f sums (and integrals). These tools have been widely used in many recent w
 orks to ensure quantitative rates of weak mixing and spectrum singularity 
 in settings such as substitution subshifts\, S-adic systems\, translations
  surfaces\, deterministic and random substitutive tilings and interval exc
 hange transformations.\n \nThe first results are obtained in the case of 
 suspension flows over Salem type substitutions. We prove Hölder decays fo
 r correlation measures in the spectral parameters belonging to the algebra
 ic field arising from the Salem number. The proof is based in a fine analy
 sis of the distribution modulo 1 of the sequence (ηα n )\, n≥0 \, wher
 e η ∈ Q(α) and α is the corresponding Salem number.\n \nThe second s
 et of results are related to the Thue-Morse substitution. We study the beh
 avior of the top Lyapunov exponents of the spectral cocycle associated to 
 the Thue-Morse substitution and its topological factors. We prove that for
  all topological factors the top Lyapunov exponent is zero\, and we also g
 ive the sub-exponential behavior of the twisted Birkhoff sums.\n\n
CATEGORIES:Séminaire,Doctorant⋅es de l'I2M
LOCATION:Saint-Charles - FRUMAM  (2ème étage)\, 3 Place Victor Hugo\, Mar
 seille\, 13003\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3 Place Victor Hugo\, Marse
 ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=Saint-Charles - FRUMAM  (
 2ème étage):geo:0,0
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