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SUMMARY:Dispersion Relations for the Nonlinear Response of Chaotic Dynamic
 al Systems - Valerio Lucarini\, Department of Physics\, University of Bolo
 gna
DTSTART:20090527T100000Z
DTEND:20090527T110000Z
UID:TALK18631@talks.cam.ac.uk
CONTACT:Dr. Fenwick Cooper
DESCRIPTION:Along the lines of the nonlinear response theory developed by 
 Ruelle\, we prove under rather general conditions that Kramers-Kronig disp
 ersion relations and sum rules apply for a class of susceptibilities descr
 ibing at any order of perturbation the response of Axiom A non equilibrium
  steady state systems to weak monochromatic forcings. We then present a nu
 merical evidence of the validity of these integral relations for the linea
 r and the second harmonic response for the perturbed Lorenz 63 system\, by
  showing that numerical simulations agree up to high degree of accuracy wi
 th the theoretical predictions. Some new theoretical results\, showing how
  to derive asymptotic behaviours and how to obtain recursively harmonic ge
 neration susceptibilities for general observables\, are also presented. Ou
 r findings confirm the conceptual validity of the nonlinear response theor
 y\, suggest that the theory can be extended for more general non equilibri
 um steady state systems\, and shed new light on the applicability of very 
 general tools\, based only upon the principle of causality\, for diagnosin
 g the behaviour of perturbed chaotic systems and reconstructing their outp
 ut signals\, in situations where the fluctuation-dissipation relation is n
 ot of great help.\n\n\n
LOCATION:Centre for Mathematical Sciences\, Meeting Room 14.
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