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UID:8791@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20251114T110000
DTEND;TZID=Europe/Paris:20251114T120000
DTSTAMP:20251103T090550Z
URL:https://www.i2m.univ-amu.fr/evenements/rauzy-2025-11-14/
SUMMARY:Yuriy TUMARKIN (Université de Zurich): Invariant sets in the wind-
 tree model
DESCRIPTION:Yuriy TUMARKIN: The wind-tree model is a billiard model of gas 
 diffusion introduced by Ehrenfest and Ehrenfest in the early 20th century.
  A small particle (the "wind") bounces between periodically placed rectang
 les (the "trees") on the plane. A lot of progress has been made in the pas
 t 15 years by studying the wind-tree model from the point of view of trans
 lation surfaces.\nIn particular\, Fraçzek and Ulcigrai proved in 2014 tha
 t in typical directions the billiard flow has no dense trajectories. This 
 opens the natural question of trying to understand what the closures of th
 e trajectories look like. The new result that I will present in this talk 
 is that in the self-similar case (when a relevant compact translation surf
 ace is periodic under renormalisation)\, all closures of trajectories have
  non-maximal Hausdorff dimension.\nThis is achieved by constructing explic
 it invariant functions for the flow\, and studying their levels sets using
  a symbolic coding for Interval Exchange Transformations.
CATEGORIES:Séminaire,Rauzy
LOCATION:Saint-Charles - FRUMAM  (2ème étage)\, 3 Place Victor Hugo\, Mar
 seille\, 13003\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3 Place Victor Hugo\, Marse
 ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=Saint-Charles - FRUMAM  (
 2ème étage):geo:0,0
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TZID:Europe/Paris
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DTSTART:20251026T020000
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