Linear response for intermittent maps with critical point
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914690768044032 |
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| author | Leppänen, Juho |
| author_facet | Leppänen, Juho |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_02310 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Linear response for intermittent maps with critical point Leppänen, Juho Dynamical Systems 37A05, 37E05 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. |
| title | Linear response for intermittent maps with critical point |
| topic | Dynamical Systems 37A05, 37E05 |
| url | https://arxiv.org/abs/2306.02310 |