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UID:6916@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20191112T110000
DTEND;TZID=Europe/Paris:20191112T120000
DTSTAMP:20241120T202625Z
URL:https://www.i2m.univ-amu.fr/evenements/guido-ahumada-dynamique-de-tran
 svections-generalisees/
SUMMARY:Guido Ahumada (IRIMAS\, Université de Haute-Alsace): Dynamique de 
 transvections généralisées
DESCRIPTION:Guido Ahumada: Given an increasing odd homeomorphism σ : {{R}}
  → {{R}}\, the two bijective maps {h}σ \, {v}σ : {{R}}2 → {{R}}2 def
 ined by\n{h}σ({x}\, {y}) = ({x} + σ-1({y})\, {y})\nand\n{v}σ({x}\, {y})
  = ({x}\, σ({x}) + {y})\nare called generalized transvections. We study t
 he action on the plane of the group Γ(σ) generated by these two maps. Pa
 rticularly interesting cases arise when σ({x}) = sgn({x})|{x}|α. We prov
 e that most points have dense orbits and that every nonzero point has a de
 nse orbit when σ({x}) = sgn({x})|{x}|2. We also look at invariant measure
 s and thanks to Nogueira's work about SL(2\, {{Z}})-invariant measure\, we
  can determine these measures when σ is linear in a neighborhood of the o
 rigin.\nJoint work with Nicolas Chevallier.\nhttps://www.researchgate.net/
 profile/Guido_Ahumada
CATEGORIES:Séminaire,Ernest
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DTSTART:20191027T020000
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