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UID:4870@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20230922T110000
DTEND;TZID=Europe/Paris:20230922T120000
DTSTAMP:20241207T131801Z
URL:https://www.i2m.univ-amu.fr/evenements/bimodal-quadratic-maps-kevin-pi
 lgrim/
SUMMARY:Kevin Pilgrim (...): Real bimodal quadratic rational maps: moduli s
 pace and entropy (with K. Filom and S. Kang)
DESCRIPTION:Kevin Pilgrim: Real bimodal quadratic rational maps: moduli spa
 ce and entropy (with K. Filom and S. Kang)\n\n&nbsp\;\n\nAbstract: Bruin-v
 an Strien and Kozlovski showed that for multimodal self-maps $f$ of the un
 it interval\, the function $f mapsto h(f)$ sending $f$ to its topological 
 entropy is monotone. K. Filom and I showed that for interval maps arising 
 from real bimodal quadratic rational maps\, this monotonicity fails. A key
  ingredient in our proof is an analysis of a family $f_{p/q}\, p/q in math
 bb{Q}/mathbb{Z}$ of critically finite maps on which the dynamics on the po
 stcritical set is conjugate to the rotation $x mapsto x+p bmod q$ on $math
 bb{Z}/qmathbb{Z}$\, where $x=0$ and $x=1$ correspond to the two critical p
 oints. The recent PhD thesis of S. Kang constructs a piecewise-linear (PL)
  copy of the well-known Farey tree whose vertices are expanding PL quotien
 ts of the $f_{p/q}$’s. This PL model\, conjecturally\, sheds light on th
 e moduli space of the real quadratic bimodal family\, and on the variation
  of entropy among such maps.
CATEGORIES:Séminaire,Rauzy
LOCATION:Saint-Charles - FRUMAM  (2ème étage)\, 3 Place Victor Hugo\, Mar
 seille\, 13003\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3 Place Victor Hugo\, Marse
 ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=Saint-Charles - FRUMAM  (
 2ème étage):geo:0,0
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