Dedicated to Klaus Hepp and Walter Hunziker for their 60th birthdays.
Abstract:Let f be a diffeomorphism of a manifold M, and ρf a (generalized) SRB state for f. If supp ρf is a hyperbolic compact set we show that the map is differentiable in a suitable functional setup, and we compute the derivative. When supp ρf is an attractor, the derivative is given by
where X is 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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: 17 October 1996 / Accepted: 26 December 1996
Rights and permissions
About this article
Cite this article
Ruelle, D. Differentiation of SRB States . Comm Math Phys 187, 227–241 (1997). https://doi.org/10.1007/s002200050134
Issue Date:
DOI: https://doi.org/10.1007/s002200050134