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SUMMARY:Elżbieta Krawczyk (Jagiellonian University)
DTSTART:20210507T081500Z
DTEND:20210507T094500Z
DTSTAMP:20260423T021929Z
UID:DSSUJ/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/DSSUJ/27/">A
 utomatic sequences in automatic systems</a>\nby Elżbieta Krawczyk (Jagiel
 lonian University) as part of Dynamical systems seminar at the Jagiellonia
 n University\n\nLecture held in 1016.\n\nAbstract\nA sequence is called au
 tomatic if it can be obtained as a coding of a fixed point of a substituti
 on of constant length. We study the class of automatic systems\, that is s
 ystems which arise as orbit closures of automatic sequences. \n\nSince the
 re are only countably many automatic sequences\, and since automatic syste
 ms usually have uncountably many points\, it is interesting to study the c
 ombinatorial structure of the subset of an automatic system which comprise
 s all of its points which are automatic. We give a dynamical description o
 f this set\, which is analogous to the one obtained by Holton and Zamboni 
 for minimal substitutive systems. In particular\, we show that automatic s
 equences in an infinite minimal automatic system correspond to the rationa
 ls in the ring of k-adic integers\, the maximal connected equicontinuous f
 actor of the system. \n\n As an application\, we show that any minimal sub
 stitutive system which factors onto an infinite k-automatic system is itse
 lf k-automatic. We also state several conjectures which generalise our res
 ults to arbitrary substitutive systems\, and explain their relation to Cob
 ham-type results (connected with the ones obtained by Durand in 2011).\n
LOCATION:https://researchseminars.org/talk/DSSUJ/27/
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