Linear response for systems with a cusp

In this talk we discuss linear response for a tent-like family of interval maps with a cusp at the singular point. we show that linear response holds for suitable perturbations of this family, in sharp contrast with the case of tent maps with finite derivative at the singularity. Our approach is based on a spectral gap for the associated transfer operators acting on Sobolev spaces $W^{1,p}$ and $W^{2,p}$.
This talk is based on:
D. Oltiboyev, Linear response for systems with a cusp, Chaos, Solitons and Fractals, 2025. https://doi.org/10.1016/j.chaos.2025.116944