Linear response for systems with a cusp

2025/05/23 by Oltiboev, Davrbek
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.17462

Abstract

In this note we consider a tent-like family with a cusp at the singular point and show that the linear response holds for certain perturbations of this family. This contrasts the tent-like maps with finite derivatives at the singularity. Our results extend the results of Bahsoun and Galatolo to the larger class of singularities and we obtain the linear response formula in L^p for p>1.

Citations

• On linear response for discontinuous perturbations of smooth endomorphisms
• Linear response for random and sequential intermittent maps
• Linear response due to singularities
• Linear response for random dynamical systems
• Linear response in the intermittent family: differentiation in a\n weighted C⁰-norm
• Linear response for intermittent maps with summable and nonsummable\n decay of correlations
• Limit theorems for coupled interval maps

Related

• Linear response due to singularities
• A Rigorous Computational Approach to Linear Response
• On linear response for discontinuous perturbations of smooth endomorphisms
• Linear response, or else
• Linear response in the intermittent family: differentiation in a\n weighted C⁰-norm