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UID:8306@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140909T110000
DTEND;TZID=Europe/Paris:20140909T120000
DTSTAMP:20241120T210330Z
URL:https://www.i2m.univ-amu.fr/evenements/fibonacci-adding-machine-and-fi
 lled-julia-set/
SUMMARY:Danilo Caprio (I2M\, Aix-Marseille Université): Fibonacci adding m
 achine and filled Julia set
DESCRIPTION:Danilo Caprio: In this work we consider a stochastic adding mac
 hine associated to the Fibonacci sequence. We obtain a Markov chain with s
 tates in N and we study some properties of the spectrum of the transition 
 operator (defined in l∞) associated to this Markov chain. In particular\
 , we prove that the spectrum of the transition operator associated to this
  Markov chain is related with the filled Julia set K = {(x\, y) ∈ ℂ² 
 : fn◦fn₋₁◦…◦f₁(x\, y) is bounded}\, where fᵢ are maps defi
 ned in ℂ² by fᵢ(x\, y) = (xy + cᵢ\, x)\, and cᵢ ∈ ℝ\, for all
  i ∈ N. More precisely\, we prove that the spectrum is equal to the set 
 S = {z ∈ ℂ : (z\, z) ∈ K}. We also show some topological properties 
 of S.\nhttps://arxiv.org/abs/1508.05062\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Danilo_Caprio.jpg
CATEGORIES:Séminaire,Ernest
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