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SUMMARY:Dan Nicks (University of Nottingham)
DTSTART:20220308T140000Z
DTEND:20220308T150000Z
DTSTAMP:20260422T201529Z
UID:CAvid/67
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/67/">I
 terating the minimum modulus</a>\nby Dan Nicks (University of Nottingham) 
 as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n
 \nAbstract\nFor an entire function $f$ there may or may not exist an $r > 
 0$ such that the iterated minimum modulus $m^n(r)$ tends to infinity. Here
  $m(r) = m(r\,f) = \\min\\{ |f(z)| : |z|=r \\}$. Focussing mainly on the c
 lass of real transcendental entire functions of finite order with only rea
 l zeroes\, we discuss some results about the existence of an $r > 0$ such 
 that $m^n(r) \\to \\infty$. This is motivated by the result that\, for fun
 ctions in this class\, the existence of such an r implies connectedness of
  the escaping set $\\{ z : f^n(z) \\to \\infty \\}$.\n\nThis is joint work
  with Phil Rippon and Gwyneth Stallard.\n
LOCATION:https://researchseminars.org/talk/CAvid/67/
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