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UID:7050@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20190510T110000
DTEND;TZID=Europe/Paris:20190510T120000
DTSTAMP:20241207T133410Z
URL:https://www.i2m.univ-amu.fr/evenements/julia-sets-for-a-class-of-polyn
 omial-maps-in-r2-and-c2-danilo-caprio/
SUMMARY:Danilo Caprio (I2M\, Aix-Marseille Université): Julia sets for a c
 lass of polynomial maps in R^2 and C^2
DESCRIPTION:Danilo Caprio: In this lecture we consider a class of endomorph
 isms of $\\mathbb{R}^2$ defined by $f(x\,y)=(xy+c\,x)$\, where $c\\in\\mat
 hbb{R}$ is a real number and we prove that when $-1&lt\;c&lt\;0$\, the for
 ward filled Julia set of $f$ is the union of stable manifolds of fixed and
  $3-$periodic points of $f$. Furthermore\, we prove that the backward fill
 ed Julia set of $f$ is the union of unstable manifolds of the saddle fixed
  and $3-$periodic points of $f$.\nWe also study the dynamics of the family
  $f_{c\,d}(x\, y) = (xy+c\, x+d)$ of endomorphisms of $\\mathbb{C}^2$\, wh
 ere $c$ and $d$ are complex parameters with $|d|&lt\;1$.\nhttps://arxiv.or
 g/search/math?searchtype=author&amp\;query=Caprio%2C+D\n\nhttps://www.rese
 archgate.net/profile/Danilo_Caprio\n\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Danilo_Caprio.jpg
CATEGORIES:Séminaire,Rauzy
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