[Settfa] Tuesday 22/11, Piotr Oprocha

[kubis at math.cas.cz]

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 Tuesday 22nd November, 11:15am 
 
  Place: IM in konírna 

 
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 Speaker:Piotr Oprocha, AGH University of Science and Technology, Krakow, Poland
 Title: On invariant sets with vanishing derivative and Cantor set dynamics

 Abstract  

 Combinatorial graphs can serve as a nice tool for description of dynamical systems on Cantor set. A classical example of this type are Bratelli- Vershik diagrams. Recently, Shimomura, motivated by works of Akin, Glasner and Weiss, developed an alternative approach, which helps to describe dynamical systems on Cantor set by employing inverse limit of graphs. This approach provides a useful tool for description of dynamical systems on Cantor set.
 

 
As a particular application of the above approach we will present a method of construction of Cantor set $C$ with prescribed dynamics and its extension to interval maps with derivative zero on $C$. Starting motivation for this study is an old question whether invariant subset $C\subset [0,1]$ on which derivative of interval map $f$ vanishes must contain a periodic point.
 

 
(joint work with Silvere Gangloff)

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .