Deutsch
 
Hilfe Datenschutzhinweis Impressum
  DetailsucheBrowse

Datensatz

DATENSATZ AKTIONENEXPORT

Freigegeben

Zeitschriftenartikel

Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables

MPG-Autoren
Es sind keine MPG-Autoren in der Publikation vorhanden
Externe Ressourcen
Es sind keine externen Ressourcen hinterlegt
Volltexte (beschränkter Zugriff)
Für Ihren IP-Bereich sind aktuell keine Volltexte freigegeben.
Volltexte (frei zugänglich)
Es sind keine frei zugänglichen Volltexte in PuRe verfügbar
Ergänzendes Material (frei zugänglich)
Es sind keine frei zugänglichen Ergänzenden Materialien verfügbar
Zitation

Kuna, T., Baladi, V., & Lucarini, V. (2017). Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables. Nonlinearity, 30(3). doi:10.1088/1361-6544/aa5b13.


Zitierlink: https://hdl.handle.net/21.11116/0000-0000-B43C-2
Zusammenfassung
We consider a smooth one-parameter family t bar right arrow (f(t) : M -> M) of diffeomorphisms with compact transitive Axiom A attractors Lambda(t), denoting by d rho(t) the SRB measure of f(t)vertical bar Lambda(t). Our first result is that for any function theta in the Sobolev space H-p(r) (M), with 1 < p < infinity and 0 < r < 1/p, the map t bar right arrow integral theta d rho(t) is alpha-Holder continuous for all alpha < r. This applies to theta(x) = h(x)Theta(g(x) - a) (for all alpha < 1) for h and g smooth and Theta the Heaviside function, if a is not a critical value of g. Our second result says that for any such function theta(x) = h(x)Theta(g(x) - a) so that in addition the intersection of {x vertical bar g(x) = a} with the support of h is foliated by 'admissible stable leaves' of ft, the map t bar right arrow integral theta d rho(t) is differentiable. (We provide distributional linear response and fluctuation-dissipation formulas for the derivative.) Obtaining linear response or fractional response for such observables theta is motivated by extreme-value theory.