Linear response for intermittent maps with critical point

2023/06/04 by Juho Leppänen, Leppänen, Juho · 1 citation
Mathematics · #37A05 #37E05 #Dynamical Systems (math.DS) #FOS: Mathematics #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2306.02310

openalex publication_date 2023/06/04 · openalex created_date 2023/06/07 · openalex updated_date 2026/07/28

Abstract

We consider a two-parameter family of maps T_{α, β}: [0,1] → [0,1] with a neutral fixed point and a non-flat critical point. Building on a cone technique due to Baladi and Todd, we show that for a class of L^q observables ϕ: [0,1] → ℝ the bivariate map (α, β) ↦ ∫₀¹ ϕ dμ_α,β, where μ_{α, β} denotes the invariant SRB measure, is differentiable in a certain parameter region, and establish a formula for its directional derivative.

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• Regularity of the variance in quenched CLT for random intermittent dynamical systems

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