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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:TALK18645@talks.cam.ac.uk
CONTACT:Doris Allen
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\nline
 ar and the second harmonic response for the perturbed Lorenz 63 system\, b
 y showing that numerical simulations agree up to high degree of accuracy w
 ith the theoretical predictions. Some new theoretical results\, showing ho
 w to derive asymptotic behaviours and how to obtain recursively harmonic g
 eneration susceptibilities for general observables\, are also presented. O
 ur findings confirm the conceptual validity of the nonlinear response theo
 ry\, suggest that the theory can be extended for more general non equilibr
 ium steady state systems\, and shed new light on the applicability of very
  general tools\, based only upon the principle of causality\, for diagnosi
 ng the behaviour of perturbed chaotic systems and\nreconstructing their ou
 tput signals\, in situations where the\nfluctuation-dissipation relation i
 s not of great help.
LOCATION:MR14\, CMS
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