Pre-threshold fractional susceptibility functions at Misiurewicz parameters. (English) Zbl 1480.37037
Summary: We show that the response, frozen and semifreddo fractional susceptibility functions of certain real-analytic unimodal families, at Misiurewicz parameters and for fractional differentiation index \(0\leqslant\eta<\frac{1}{2}\), are holomorphic on a disk of radius greater than one. This is a step towards solving a conjecture of V. Baladi and D. Smania [Commun. Math. Phys. 385, No. 3, 1957–2007 (2021; Zbl 1478.37044)], in the case of the aforementioned susceptibility functions.
MSC:
| 37C30 | Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. |
| 37C40 | Smooth ergodic theory, invariant measures for smooth dynamical systems |
| 37E05 | Dynamical systems involving maps of the interval |
| 37A10 | Dynamical systems involving one-parameter continuous families of measure-preserving transformations |
Citations:
Zbl 1478.37044References:
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