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SUMMARY:Michel Zinsmeister (Université d'Orléans\, France)
DTSTART:20230314T130000Z
DTEND:20230314T140000Z
DTSTAMP:20260422T201743Z
UID:CAvid/101
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/101/">
 Coullet-Tresser Cascade of Bifurcations in the logistic Family and Hausdor
 ff Dimension of real quadratic Julia Sets</a>\nby Michel Zinsmeister (Univ
 ersité d'Orléans\, France) as part of CAvid: Complex Analysis video semi
 nar\n\nLecture held in N/A.\n\nAbstract\nIn a paper with L. Jacksztas (Adv
  Math 2020) we have proven that if $c_0$ is a parabolic parameter (i.e. wi
 th a parabolic cycle) in $(c_{Feig}\,1/4)$ ($c_{Feig}$ being the limit poi
 nt of the cascade of bifurcations) then the function $d(c)=$ Hausdorff dim
 ension of the Julia set $J_c$ of $z^2+c$ has an infinite derivative at $c_
 0$ if $d(c_0)\\leq 4/3$\, while it is $C^1$ across $c_0$ if $d(c_0)>4/3$.\
 n\nRecently A. Dudko\, I. Gorobovickis and W. Tucker have proven that $d(c
 )>4/3$ on $[-1.53\,-1.23]$ (arXiv:2204.07880). The combination of these tw
 o results implies that $d$ is $C^1$ on $(c_{Feig}\,-3/4)$ while $d'(-3/4)=
 -\\infty$ (a former result of L. Jacksztas).\\\\\nAfter some description (
 including a history) of the Coullet-Tresser Feigenbaum phenomenon\, I will
  outline the proof of J-Z theorem and briefly describe D-G-T's result. \n\
 n(Joint work with L. Jacksztas)\n
LOCATION:https://researchseminars.org/talk/CAvid/101/
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