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SUMMARY:Differentiations and Diversions - Michael Berry (University of Bri
 stol)
DTSTART:20210330T150000Z
DTEND:20210330T160000Z
UID:TALK158383@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Asymptotic procedures\, such as generating slowness<br><br> co
 rrections to geometric phases\, involve successive differentiations. For a
 <br><br> large class of functions\, the universal attractor of the differe
 ntiation map is\,<br><br> when suitably scaled\, locally trigonometric/exp
 onential\; nontrivial examples<br><br> illustrate this. For geometric phas
 es\, the series must diverge\, reflecting the<br><br> exponentially small 
 final transition amplitude. Evolution of the amplitude<br><br> towards thi
 s final velue depends sensitively on the representation used. If<br><br> t
 his is optimal\, the transition takes place rapidly and universally across
  a<br><br> Stokes line emanating from a degeneracy in the complex time pla
 ne. But some<br><br> Hamiltonian ODE systems do not generate transitions\;
  this is because the<br><br> complex-plane degeneracies have a peculiar st
 ructure\, for which there is no<br><br> Stokes phenomenon.&nbsp\; Oscillat
 ing high<br><br> derivatives (asymptotic monochromaticity) and superoscill
 ations (extreme<br><br> polychromaticity) are in a sense opposite mathemat
 ical phenomena.<br><br> <br><br> <br><br><br><br><br>
LOCATION:Seminar Room 1\, Newton Institute
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