Abstract
The SRB measures of a hyperbolic system are widely accepted as the measures that are physically relevant. It has been shown by Ruelle that they depend smoothly on the system. Furthermore, Ruelle showed by a separate argument that the first derivative, i.e., the linear response function, admits a geometric interpretation. In this paper, we consider thermodynamic limits of SRB measures in lattices of coupled hyperbolic attractors. In a previous paper, using Markov partitions and thermodynamic formalism, we had established the smooth dependence of thermodynamic limits of SRB measures. Here, we establish that the linear response function admits a geometric interpretation. The formula is analogous to the one found by Ruelle for finite dimensional systems if one term is reinterpreted appropriately. We show that the limiting derivative is the thermodynamic limit of the derivatives in finite volume. We also obtain similar results for the derivatives of the entropy.
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