Establishes quenched and annealed linear response and statistical stability for partially hyperbolic skew products with parameter-dependent base maps, yielding new formulas for the response and moment derivatives.
On linear response for discontinuous perturbations of smooth endomorphisms
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We consider discontinuous perturbations of smooth endomorphisms and show that if the perturbed family satisfies uniform mixing assumptions on standard pairs the physical measure is Lipschitz in the parameter defying the perturbation. We also study the problem of linear response for this class of perturbations. Finally we discuss the applicability of the abstract assumptions proving linear response for a concrete example.
fields
math.DS 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
The conditional survival probability measure for Sinai billiards with small holes is differentiable at t=0 and its derivative is computed.
citing papers explorer
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Quenched and annealed linear response for some partially hyperbolic skew products
Establishes quenched and annealed linear response and statistical stability for partially hyperbolic skew products with parameter-dependent base maps, yielding new formulas for the response and moment derivatives.
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Linear response for Sinai billiards with small holes
The conditional survival probability measure for Sinai billiards with small holes is differentiable at t=0 and its derivative is computed.