<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML><HEAD>
<META http-equiv=Content-Type content="text/html; charset=iso-8859-1">
<META content="MSHTML 6.00.6000.17092" name=GENERATOR>
<STYLE></STYLE>
</HEAD>
<BODY bgColor=#ffffff>
<DIV><FONT face=Arial size=2>
<P class=MsoTitle style="MARGIN: 0cm 0cm 0pt" align=center><SPAN
style="FONT-SIZE: 18pt; FONT-FAMILY: 'Times New Roman','serif'"><STRONG><U>SEMINARIO
DI <SPAN style="mso-no-proof: yes">SISTEMI DINAMICI</SPAN><?xml:namespace prefix
= o ns = "urn:schemas-microsoft-com:office:office"
/><o:p></o:p></U></STRONG></SPAN></P>
<H2 style="MARGIN: 0cm 0cm 0pt 9pt" align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes"></SPAN> </H2>
<H2 style="MARGIN: 0cm 0cm 0pt 9pt" align=center><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes">mercoledì 20
ottobre 2010</SPAN><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'"><o:p></o:p></SPAN></H2>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">ore <SPAN
style="mso-no-proof: yes">16.00</SPAN><o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN style="FONT-FAMILY: 'Times New Roman','serif'"><o:p><FONT
size=3> </FONT></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><U><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Scuola Normale
Superiore<o:p></o:p></SPAN></U></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Pisa<o:p></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt 9pt; LINE-HEIGHT: 18pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">(Sala Conferenze
Collegio Puteano)<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"><B
style="mso-bidi-font-weight: normal"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes"><o:p><FONT
size=3> </FONT></o:p></SPAN></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><B style="mso-bidi-font-weight: normal"><SPAN
style="FONT-SIZE: 22pt; FONT-FAMILY: 'Times New Roman','serif'; mso-no-proof: yes">Viviane
Baladi</SPAN></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><SPAN><EM><FONT face="Times New Roman">CNRS, E.N.S.
Paris<o:p></o:p></FONT></EM></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 324.0pt"
align=left><SPAN style="FONT-FAMILY: 'Times New Roman','serif'"><o:p><FONT
size=3></FONT></o:p></SPAN></P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'"></SPAN> </P>
<P class=MsoNormal
style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center; tab-stops: 324.0pt"
align=center><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Terrà un
seminario dal titolo:<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; tab-stops: 324.0pt"><SPAN
style="FONT-FAMILY: 'Times New Roman','serif'"><o:p><FONT
size=3> </FONT></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 22pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB">“</SPAN></I></B><B
style="mso-bidi-font-weight: normal"><SPAN lang=EN-US
style="FONT-SIZE: 22pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">Linear
response for generic smooth unimodal maps</SPAN></B><B
style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 22pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB">”<SPAN
style="mso-no-proof: yes"><o:p></o:p></SPAN></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: center"
align=center><SPAN lang=EN-US
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">(Joint
with Daniel Smania)<o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
lang=EN-US
style="FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US"><o:p><FONT
size=3> </FONT></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-US
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-US">Many
interesting dynamical systems admit a "natural" or "physical" measure, which
describes the asymptotic time averages of a positive Lebesgue measure set of
initial conditions. This measure is called the SRB measure, for
Sinai-Ruelle-Bowen. When a smooth one-parameter family f_t of dynamical systems
admits for all (or many) small paramerers t a unique SRB measure mu_t, it is
natural to ask if the map t -> mu_t is also smooth(possibly in the sense of
Whitney). In 1997, David Ruelle solved the case when the f_t are smooth and
uniformly hyperbolic, obtaining a formula for the derivative: the linear
response formula.Ten years later, Daniel Smania and I discovered by studying a
"toy model" (piecewise expanding maps) that the presence of critical points
(which destroy structural stability) may cause obstructions to linear response.
We proved that the condition of "tangency" of the family to the topological
class was necessary and sufficient for linear response to hold. For smooth
nonuniformly hyperbolic unimodal maps, the situation is much more difficult, and
for the moment one only considers families f_t which remain in the topological
class of f_0. Up to 2009, only (nongeneric) situations very close to hyperbolic
had been tackled (Ruelle, B-Smania). We shall present a recent joint result with
Daniel Smania (available on arxiv.org), which holds under a generic recurrence
condition.</SPAN></I><B style="mso-bidi-font-weight: normal"><I
style="mso-bidi-font-style: normal"><SPAN lang=EN-GB
style="FONT-SIZE: 11pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB"><o:p></o:p></SPAN></I></B></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
lang=EN-GB
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
lang=EN-GB
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: EN-GB"><o:p> </o:p></SPAN></P>
<P class=MsoNormal style="MARGIN: 0cm 0cm 0pt; TEXT-ALIGN: justify"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'">Tutti gli
interessati sono invitati a partecipare.<o:p></o:p></SPAN></P>
<P class=MsoBodyText style="MARGIN: 0cm 0cm 0pt; tab-stops: 9.0cm"><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: IT"><o:p> </o:p></SPAN></P>
<P class=MsoBodyText style="MARGIN: 0cm 0cm 0pt; tab-stops: 9.0cm"><FONT
face="Times New Roman"><SPAN lang=EN-GB><SPAN style="mso-tab-count: 2"><FONT
size=3>
</FONT></SPAN></SPAN><SPAN
style="FONT-SIZE: 16pt; FONT-FAMILY: 'Times New Roman','serif'; mso-ansi-language: IT">Classe
di Scienze<o:p></o:p></SPAN></FONT></P></FONT></DIV>
<DIV><FONT face=Arial
size=2>--------------------------------------------------------------------------------<BR>Valeria
Giuliani<BR>Scuola Normale Superiore<BR>Servizio Supporto Attività Didattiche -
Scienze<BR>Tel. 050-509260<BR>Fax. 050-509045<BR>Piazza dei Cavalieri,
7<BR>56126 Pisa<BR>E-Mail: <A
href="mailto:v.giuliani@sns.it">v.giuliani@sns.it</A> <BR>E-Mail: <A
href="mailto:segreteria.scienze@sns.it">segreteria.scienze@sns.it</A></FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2>Le informazioni contenute nella presente e-mail e
nei relativi allegati possono essere riservate e sono, comunque, destinate
esclusivamente al destinatario in indirizzo.<BR>E’ vietata, pertanto, la
diffusione, distribuzione e/o copiatura di tali informazioni da parte di
qualsiasi soggetto diverso dal destinatario. <BR>Chiunque abbia ricevuto o letto
questa e-mail per errore o senza esserne legittimato è invitato a darne
immediatamente notizia al mittente tramite fax o e-mail e a
distruggerla.<BR>Grazie.</FONT></DIV>
<DIV> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV></BODY></HTML>