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UID:8348@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140603T110000
DTEND;TZID=Europe/Paris:20140603T120000
DTSTAMP:20241120T210344Z
URL:https://www.i2m.univ-amu.fr/evenements/graph-theoretic-structure-of-ma
 ps-of-the-cantor-space/
SUMMARY:Udayan B. Darji (University of Louisville\, USA): Graph theoretic s
 tructure of maps of the Cantor space
DESCRIPTION:Udayan B. Darji: We develop unifying graph theoretic techniques
  to study the dynamics and the structure of spaces H({0\, 1}^ℕ) and C({0
 \, 1}^ℕ)\, the space of homeomorphisms and the space of self-maps of the
  Cantor space\, respectively. Using our methods\, we give characterization
 s which determine when two homeomorphisms of the Cantor space are conjugat
 e to each other. We also give a new characterization of the comeager conju
 gacy class of the space H({0\, 1}^ℕ). The existence of this class was es
 tablished by Kechris and Rosendal and a specific element of this class was
  described concretely by Akin\, Glasner and Weiss. Our characterization re
 adily implies many old and new dynamical properties of elements of this cl
 ass. For example\, we show that no element of this class has a Li–Yorke 
 pair\, implying the well known Glasner–Weiss result that there is a come
 ager subset of H({0\, 1}^ℕ) each element of which has topological entrop
 y zero. Our analogous investigation in C({0\, 1}^ℕ) yields a surprising 
 result: there is a comeager subset of C({0\, 1}^ℕ) such that any two ele
 ments of this set are conjugate to each other by an element of H({0\, 1}^
 ℕ). Our description of this class also yields many old and new results c
 oncerning dynamics of a comeager subset of C({0\, 1}^ℕ).\nhttps://www.sc
 iencedirect.com/science/article/pii/S0001870812002551\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Udayan_Darji.jpg
CATEGORIES:Séminaire,Ernest
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