Linear response for intermittent maps with critical point

Juho Leppänen

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arXiv · 2306.02310

Linear response for intermittent maps with critical point

Juho Leppänen

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Abstract

We consider a two-parameter family of maps $T_{α, β}: [0,1] \to [0,1]$ 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 $ϕ: [0,1] \to \mathbb{R}$ the bivariate map $(α, β) \mapsto \int_0^1 ϕ\, dμ_{α,β}$, 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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BibTeX RIS

Juho Leppänen. 2024-02-25. Linear response for intermittent maps with critical point. https://arxiv.org/abs/2306.02310

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