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SUMMARY:Till Hausner (FSU Jena)
DTSTART:20201127T091500Z
DTEND:20201127T104500Z
DTSTAMP:20260423T021858Z
UID:DSSUJ/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/DSSUJ/14/">E
 ntropy in the context of aperiodic order</a>\nby Till Hausner (FSU Jena) a
 s part of Dynamical systems seminar at the Jagiellonian University\n\nLect
 ure held in 1016.\n\nAbstract\nIn this talk we study different notions of 
 entropy for\nDelone sets of finite local complexity in the setting of (met
 rizable\nand sigma-compact) locally compact Abelian groups (LCA groups).\n
 \nFor Delone sets of finite local complexity (FLC) in the euclidean\nspace
  it is well known that the patch counting entropy equals the\ntopological 
 entropy of an associated shift system. We present an\nexample of a FLC Del
 one set in a LCA group for which the topological\nentropy and the patch co
 unting entropy are not equal.\n\nIt was suggested by J. Lagarias for FLC D
 elone sets in the euclidean\nspace that the patch counting entropy can alw
 ays be computed as a\nlimit. We discuss why the Ornstein-Weiss lemma can n
 ot directly be\nused in order to see this claim and present that the corre
 spondence\nbetween the topological and the patch counting entropy can be u
 sed in\norder to show that the limit in the patch counting entropy formula
 \nexists for compactly generated LCA groups. We present counterexamples\nw
 here the limit does not exist in the context of general LCA groups.\n
LOCATION:https://researchseminars.org/talk/DSSUJ/14/
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