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SUMMARY:Breakdown of linear response in the presence of bifurcations - Bal
 adi\, V (CNRS and Ecole Normale Suprieure\, Paris)
DTSTART:20131112T100000Z
DTEND:20131112T110000Z
UID:TALK48788@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:(Joint with: M. Benedicks and D. Schnellmann) Many interesting
  dynamical systems possess a unique SRB ("physical") measure\, which behav
 es well with respect to Lebesgue measure. Given a smooth one-parameter fam
 ily of dynamical systems f_t\, is natural to ask whether the SRB measure d
 epends smoothly on the parameter t. If the f_t are smooth hyperbolic diffe
 omorphisms (which are structurally stable)\, the SRB measure depends diffe
 rentiably on the parameter t\, and its derivative is given by a "linear re
 sponse" formula (Ruelle\, 1997). When bifurcations are present and structu
 ral stability does not hold\, linear response may break down. This was fir
 st observed for piecewise expanding interval maps\, where linear response 
 holds for tangential families\, but where a modulus of continuity t log t 
 may be attained for transversal families (Baladi-Smania\, 2008). The case 
 of smooth unimodal maps is much more delicate. Ruelle (Misiurewicz case\, 
 2009) and Baladi-Smania (slow recurrence case\, 2012) obtained linear resp
 onse for fully tangential families (confined within a topological class). 
 The talk will be nontechnical and most of it will be devoted to motivation
  and history. We also aim to present our new results on the transversal sm
 ooth unimodal case (including the quadratic family)\, where we obtain Hold
 er upper and lower bounds (in the sense of Whitney\, along suitable classe
 s of parameters).\n
LOCATION:Seminar Room 1\, Newton Institute
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