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UID:6426@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20210506T140000
DTEND;TZID=Europe/Paris:20210506T150000
DTSTAMP:20250118T133037Z
URL:https://www.i2m.univ-amu.fr/evenements/linearization-of-transseries-an
 d-transserial-maps-in-a-neighborhood-of-a-singular-point/
SUMMARY:Jean-Philippe Rolin (Institut de Mathématiques de Bourgogne\, Dijo
 n): Linearization of transseries and transserial maps in a neighborhood of
  a singular point
DESCRIPTION:Jean-Philippe Rolin: It is known since Schröder (1873) that in
  order to study the iterations of a function in the neighborhood of a fixe
 d point (which can be seen as a singularity of the system in this context)
 \, the best way\, when possible\, is to linearize the function\, that is t
 o find a coordinate in which the function becomes a linear map. The linear
 ization problem has been solved by Koenigs for holomorphic maps in one var
 iable under the hypothesis of "hyperbolicity". This result has been extend
 ed to several category of differentiable functions.\nOur goal is to show a
  version of this result in the framework of "transseries"\, which are form
 al power series involving the exponential and logarithm functions. The pro
 of investigates valuations and various topologies on the class of transser
 ies. This result has an application in the dynamics of so-called Dulac map
 s\, which play a important role in a celebrated conjecture on planar polyn
 omial vector fields. Joint with D. Peran\, M. Resman and T. Servi.\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 021/04/Jean-Philippe_Rolin.jpg
CATEGORIES:Groupe de travail,Singularités,Virtual event
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