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UID:20251019T032305EDT-1886D2herT@132.216.98.100
DTSTAMP:20251019T072305Z
DESCRIPTION:Given two commuting transformations σ\, Φ : X → X acting on a c
 ompact metric space\, what are the measures on X which are invariant under
  the action of σ and Φ? This general question includes the open problem po
 sed by Furstenberg\, which is to find the measures on the unit interval wh
 ich are invariant under both x 1→ 2x mod 1 and x → 3x mod 1. Let p be a pr
 ime number and let Fp be the field of cardinality p. A linear cellular aut
 omaton Φ : FZ → FZ is an Fp-linear map that commutes with the (left) shift
  map σ : FZ → FZ. A famous linear cellular automaton is Ledrappier’s\, def
 ined by p p Φ(x) = x + σ(x)\, where\, in contrast to a symbolic version of
  Furstenberg’s question\, addition is performed “bitwise” and without carr
 y. For a linear cellular automaton Φ\, examples of measures which are (Φ\,
  σ)- invariant are the uniform measure on FZ\, and measures supported on a
  finite set. In work by Einsiedler from the early 2000’s\, if we recast li
 near cellular automata in the setting of Markov subgroups\, we find a new 
 family of nontrivial (σ\, Φ)-invariant measures. In recent joint work with
  Eric Rowland\, we find another family of of nontrivial (σ\, Φ)-invariant 
 measures\, using constant length substitutions\, and their characterisatio
 n by Christol. I will describe how we obtain these measures\, and compare 
 them to Einsiedler’s construction.\n
DTSTART:20190906T173000Z
DTEND:20190906T183000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Reem Yassawi (Open University)
URL:/mathstat/channels/event/reem-yassawi-open-univers
 ity-300256
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