On the fractional susceptibility function of piecewise expanding maps

Magnus Aspenberg, Viviane Baladi, Juho Leppänen, Tomas Persson

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskriftPeer review

Sammanfattning

We associate to a perturbation (ft) of a (stably mixing) piecewise expanding unimodal map f0 a two-variable fractional susceptibility function Ψφ(η, z), depending also on a bounded observable φ. For fixed η ∈ (0, 1), we show that the function Ψφ(η, z) is holomorphic in a disc Dη ⊂ C centered at zero of radius > 1, and that Ψφ(η, 1) is the Marchaud fractional derivative of order η of the function t 7→ Rφ(t):= R φ(x) dµt, at t = 0, where µt is the unique absolutely continuous invariant probability measure of ft. In addition, we show that Ψφ(η, z) admits a holomorphic extension to the domain {(η, z) ∈ C2 | 0 < <η < 1, z ∈ Dη }. Finally, if the perturbation (ft) is horizontal, we prove that limη(0,1),η→1 Ψφ(η, 1) = ∂tRφ(t)|t=0.

Originalspråkengelska
Sidor (från-till)679-708
Antal sidor30
TidskriftDiscrete and Continuous Dynamical Systems- Series A
Volym42
Utgåva2
DOI
StatusPublished - 2022 feb.

Ämnesklassifikation (UKÄ)

  • Matematisk analys

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