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UID:6939@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20191018T110000
DTEND;TZID=Europe/Paris:20191018T120000
DTSTAMP:20241207T133604Z
URL:https://www.i2m.univ-amu.fr/evenements/rigidity-of-newton-dynamics-kos
 tiantyn-drach/
SUMMARY:Kostiantyn Drach (I2M Aix-Marseille University and V. N. Karazin Kh
 arkiv National University): Rigidity of Newton dynamics
DESCRIPTION:Kostiantyn Drach: The Newton map of a complex polynomial is a r
 ational map coming from Newton's root-finding method. This is "a map that 
 wants to be iterated"\, as the numerical method suggests. From the point o
 f view of complex dynamics\, the Newton maps of degree d&gt\;2 form an imp
 ortant family of rational maps\, arguably the largest family (beyond polyn
 omials) that gained our substantial level of understanding in recent years
 . We contribute to this development by studying rigidity properties of New
 ton maps of arbitrary degree. One of our key results is that any two combi
 natorially equivalent Newton maps are quasi-conformally conjugate provided
  that they are either non-renormalizable\, or renormalizable in the same w
 ay. In other words\, Newton maps can be distinguished among each other in 
 purely combinatorial terms modulo "embedded" polynomial dynamics. A simila
 r statement in the dynamical plane ("dynamical" rigidity of Newton maps) a
 lso holds true. In the talk\, we will outline the proofs of the aforementi
 oned results with an emphasis on the construction of puzzle pieces for New
 ton maps. This is an important step because it allows us to employ the met
 hods of symbolic dynamics in the spirit of celebrated Yoccoz puzzles\, and
  the results on rigidity of polynomials (by Yoccoz\, Kahn-Lyubich\, Kozlov
 ski-Shen-van Strien and others). Based on joint work with Dierk Schleicher
 .\n\nhttp://geometry.karazin.ua/en/~drach\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Kostiantyn_Drach.jpg
CATEGORIES:Séminaire,Rauzy
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DTSTART:20190331T030000
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