BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//wp-events-plugin.com//7.2.3.1//EN
TZID:Europe/Paris
X-WR-TIMEZONE:Europe/Paris
BEGIN:VEVENT
UID:7397@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20180130T110000
DTEND;TZID=Europe/Paris:20180130T120000
DTSTAMP:20241120T203940Z
URL:https://www.i2m.univ-amu.fr/evenements/nilpotent-endomorphisms-of-expa
 nsive-group-actions/
SUMMARY:Ilkka Törmä (University of Turku\, Finland): Nilpotent endomorphi
 sms of expansive group actions
DESCRIPTION:Ilkka Törmä: Consider a cellular automaton with a special qui
 escent state 0. The automaton is called nilpotent if it sends every initia
 l configuration to the 0-uniform configuration in a bounded number of step
 s. It is asymptotically nilpotent if the forward orbit of every configurat
 ion converges toward the 0-uniform configuration in the product topology. 
 Guillon and Richard showed in 2008 that on a one-dimensional full shift\, 
 these notions are equivalent. In 2012\, Salo extended the result to multid
 imensional full shifts.\n\nWe further generalize these results to the sett
 ing of expansive group actions. More formally\, given a continuous action 
 of a group G on a compact metric space X and a single fixed point 0∈X\, 
 one can ask whether there exists an endomorphism f:X→X such that fⁿ(x)
 ⟶0 for every x∈X\, but the convergence is not uniform. We focus on exp
 ansive actions that have dense 0-homoclinic points and a specification-lik
 e property that we call 0-gluing. For example\, every strongly irreducible
  G-SFT with a uniform configuration satisfies these conditions. We show th
 at for a large class of groups\, containing in particular all residually f
 inite solvable groups\, and all such actions on them\, all asymptotically 
 nilpotent endomorphisms exhibit uniform convergence. In the course of the 
 proof\, we develop a technical tool called a tiered dynamical system\, whi
 ch consists of a nested family of compact subsets of an ambient space\, ea
 ch of which is equipped with a group action. (Joint work with Ville Salo).
 \nhttps://arxiv.org/abs/1804.07630\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/IIkka_Torma.jpg
CATEGORIES:Séminaire,Ernest
END:VEVENT
BEGIN:VTIMEZONE
TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:STANDARD
DTSTART:20171029T020000
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
END:STANDARD
END:VTIMEZONE
END:VCALENDAR