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UID:4885@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20231003T110000
DTEND;TZID=Europe/Paris:20231003T120000
DTSTAMP:20240610T125805Z
URL:https://www.i2m.univ-amu.fr/evenements/brjuno-functions-and-holder-con
 tinuity/
SUMMARY:Stefano Marmi (Scuola Normale di Pisa): Brjuno functions and Hölde
 r continuity
DESCRIPTION:Stefano Marmi: In 1988 Yoccoz proved that the size of the stabi
 lity domain (Siegel disk) around an irrationally indifferent fixed point i
 n the complex plane is given by a purely arithmetic function -called Brjun
 o's function- up to a more regular (L^∞) correction. The Hölder interpo
 lation conjecture (aka Marmi-Moussa-Yoccoz conjecture) states that for qua
 dratic polynomials this correction is in fact ½-Hölder-continuous. An an
 alogous version of the conjecture stands also for other dynamical systems\
 , including the standard family. Hölder continuity seems to be the releva
 nt regularity for these problems also since it measures the difference bet
 ween formulations of the arithmetical function corresponding to different 
 continued fraction algorithms (Gauss\, nearest integer\, by-excess\, …).
  The talk will be based on recent work in collaboration with Seul Bee Lee.
CATEGORIES:Séminaire,Ernest
LOCATION:I2M Luminy - Ancienne BU\, Salle Séminaire2 (RdC)\, 163 Avenue de
  Luminy\, 13009 Marseille\, France\, 
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, 1300
 9 Marseille\, France\, ;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - Ancienne B
 U\, Salle Séminaire2 (RdC):geo:0,0
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