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SUMMARY:When hyperbolic maps are matings.
DTSTART;VALUE=DATE-TIME:20171024T151500Z
DTEND;VALUE=DATE-TIME:20171024T161000Z
DTSTAMP;VALUE=DATE-TIME:20220524T003949Z
UID:indico-contribution-1260@indico.math.cnrs.fr
DESCRIPTION:Speakers: Mary Rees (University of Liverpool)\nA mating is a r
ational map made by combining two polynomials of the same degree in a cert
ain fashion. Matings were a recurring theme in Tan Lei's work\, not surpri
singly\, since the concept was invented by Douady and Hubbard after their
extraordinary success in describing the Mandelbrot set in the parameter s
pace of quadratic polynomials. in fact\, Tan Lei's thesis was essentially
an existence result\, prompted by a question of Douady\, and showing that
matings are in plentiful supply. It was\, however\, realised early on that
not all rational maps can be described in terms of matings of polynomials
. Nevertheless\, there are regions of the parameter space of quadratic ra
tional maps in which matings do give a good combinatorial description of t
he parameter space\, and describe all hyperbolic rational maps of bitransi
tive type. I will talk about a relatively new instance of this\, in the ca
se where all Fatou components have disjoint closures.\n\nhttps://indico.ma
th.cnrs.fr/event/2284/contributions/1260/
LOCATION:Université d'Angers L003.
URL:https://indico.math.cnrs.fr/event/2284/contributions/1260/
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