2023/01/05 by Wael Bahsoun, Stefano Galatolo, Bahsoun, Wael +1 · 1 citation
Mathematics · Physics and Astronomy · #37A05 #37E05 #Advanced Differential Equations and Dynamical Systems #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2301.02301
openalex publication_date 2023/01/05 · openalex created_date 2023/01/10 · openalex updated_date 2026/07/28
It is well known that a family of tent-like maps with bounded derivatives has no linear response for typical deterministic perturbations changing the value of the turning point. In this note we prove the following result: if we consider a tent-like family with a cusp at the turning point, we recover the linear response. More precisely, let T_\eps be a family of such cusp maps generated by changing the value of the turning point of T0 by a deterministic perturbation and let h_\eps be the corresponding invariant density. We prove that \eps↦ h_\eps is differentiable in L1 and provide a formula for its derivative.