Abstract
Let M be a smooth Riemannian manifold. We show that for C 1 generic \({f\in {\rm Diff}^1(M)}\), if f has a hyperbolic attractor Λ f , then there exists a unique SRB measure supported on Λ f . Moreover, the SRB measure happens to be the unique equilibrium state of potential function \({\psi_f\in C^0(\Lambda_f)}\) defined by \({\psi_f(x)=-\log|\det(Df|E^u_x)|, x\in \Lambda_f}\), where \({E^u_x}\) is the unstable space of T x M.
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Communicated by G. Gallavotti
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Qiu, H. Existence and Uniqueness of SRB Measure on C 1 Generic Hyperbolic Attractors. Commun. Math. Phys. 302, 345–357 (2011). https://doi.org/10.1007/s00220-010-1160-2
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DOI: https://doi.org/10.1007/s00220-010-1160-2