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SUMMARY:Phil Rippon (Open University\, UK)
DTSTART:20200908T130000Z
DTEND:20200908T140000Z
DTSTAMP:20260422T201549Z
UID:CAvid/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CAvid/11/">C
 onstructing entire functions of small order - motivated by complex dynamic
 s</a>\nby Phil Rippon (Open University\, UK) as part of CAvid: Complex Ana
 lysis video seminar\n\nLecture held in N/A.\n\nAbstract\nIn 1989\, Eremenk
 o conjectured that for any transcendental entire function the escaping set
  $I(f) = \\{z:f^n(z)\\to\\infty \\text{ as } n\\to\\infty\\}$ has no bound
 ed components -- despite much work this conjecture is still open.\n\nFor r
 eal entire functions $f$ of finite order with only real zeros\, we have sh
 own that Eremenko's conjecture holds if there exists $r>0$ such that the i
 terated minimum modulus $m^n(r)\\to\\infty$ as $n\\to\\infty$. Here $m(r)=
 \\min_{|z|=r}|f(z)|$.\n\nWe discuss examples of families of entire functio
 ns of small order for which this iterated minimum modulus condition holds\
 , and construct examples of functions of small order for which it does not
  hold\, including examples based on a new development of a method due to K
 jellberg.\n\n(Joint work with Dan Nicks and Gwyneth Stallard.)\n\nPlease e
 -mail Rod Halburd (r.halburd@ucl.ac.uk) for the Zoom link.  Please let him
  know if you would like to receive weekly announcements about CAvid (the C
 omplex Analysis video seminar series).\n
LOCATION:https://researchseminars.org/talk/CAvid/11/
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