On invariant sets with vanishing derivative and Cantor set dynamics

Piotr Oprocha
AGH University of Science and Technology in Kraków

Date(s) : 24/05/2022   iCal
11 h 00 min - 12 h 00 min

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⊂[0,1]$ on which derivative of interval map f vanishes must contain a periodic point.

(joint work with Silvère Gangloff)

Site Sud, Luminy, Ancienne BU, Salle Séminaire2 (RdC)


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