Linear response for intermittent maps with summable and nonsummable\n decay of correlations

2015/08/26 by Alexey Korepanov, Korepanov, Alexey · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1508.06571

openalex publication_date 2015/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a family of Pomeau-Manneville type interval maps T_\α,\nparametrized by \α \∈ (0,1), with the unique absolutely continuous\ninvariant probability measures \ν_\α, and rate of correlations decay\nn^1-1/\α. We show that despite the absence of a spectral gap for all\n\α \∈ (0,1) and despite nonsummable correlations for \α \≥ 1/2,\nthe map \α \↦ \∫ \φ , d\ν_\α is continuously\ndifferentiable for \φ \∈ L^q[0,1] for q sufficiently large.\n

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