Linear response formula for piecewise expanding unimodal maps
نویسندگان
چکیده
منابع مشابه
Linear Response Formula for Piecewise Expanding Unimodal Maps
The average R(t) = R φdμt of a smooth function φ with respect to the SRB measure μt of a smooth one-parameter family ft of piecewise expanding interval maps is not always Lipschitz [4], [17]. We prove that if ft is tangent to the topological class of f , and if ∂tft|t=0 = X ◦ f , then R(t) is differentiable at zero, and R(0) coincides with the resummation proposed in [4] of the (a priori diverg...
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We give two new proofs that the SRB measure t 7→ μt of a C path ft of unimodal piecewise expanding C maps is differentiable at 0 if ft is tangent to the topological class of f0. The arguments are more conceptual than the one in [4], but require proving Hölder continuity of the infinitesimal conjugacy α (a new result, of independent interest) and using spaces of bounded p-variation. The first ne...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2008
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/21/4/003