Differentiation of SRB States
Differentiation of SRB States
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DOI：
10.1007/s002200050134
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发表时间：
1997-07
影响因子：
2.4
通讯作者：
D. Ruelle
中科院分区：
文献类型：
--
作者：
D. Ruelle
本文献给Klaus Hepp和Walter Hunziker，祝贺他们60岁生日。 如果supp ρ f是双曲紧集，我们证明该映射 在适当的函数设置中是可微的，我们计算导数。 当supp ρ f是吸引子时，导数由下式给出其中X是向量场 . 这个公式可以推广到依赖于时间的情形，至少形式上也可以推广到非一致双曲的情形，上述结果将用于研究非平衡统计力学的Onsager互易关系和涨落耗散公式。
Dedicated to Klaus Hepp and Walter Hunziker for their 60th birthdays.Abstract:Letfbe a diffeomorphism of a manifoldM, and ρfa (generalized) SRB state forf. If supp ρfis a hyperbolic compact set we show that the map is differentiable in a suitable functional setup, and we compute the derivative. When supp ρfis an attractor, the derivative is given by whereXis the vector field . This formula can be extended to time dependent situations and also, at least formally, to nonuniformly hyperbolic situations.The above results will find their use in the study of the Onsager reciprocity relations and the fluctuation-dissipation formula of nonequilibrium statistical mechanics.