We consider a wide family of non-uniformly expanding maps and hyperbolic Hölder continuous potentials. We prove that the unique equilibrium state associated to each element of this family is given by the eigenfunction of the transfer operator and the eigenmeasure of the dual operator (both having the spectral radius as eigenvalue). We show that the transfer operator has the spectral gap property in some space of Hölder continuous observables and from this we obtain an exponential decay of correlations and a central limit theorem for the equilibrium state. Moreover, we establish the analyticity with respect to the potential of the equilibrium state as well as that of other thermodynamic quantities. Furthermore, we derive similar results for the equilibrium state associated to a family of non-uniformly hyperbolic skew products and hyperbolic Hölder continuous potentials.

中文翻译：

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非均匀双曲系统的平衡态：统计性质和解析性

我们考虑了各种不均匀扩展的图谱和双曲线荷尔德连续势。我们证明，与该族的每个元素相关的唯一平衡态是由转移算子的本征函数和对偶算子的本征测度（均以谱半径作为本征值）给出的。我们证明了转移算子在Hölder连续可观测量的某些空间中具有谱隙性质，由此我们可以得出相关性的指数衰减和平衡态的中心极限定理。此外，我们建立了关于平衡态势以及其他热力学量的解析性。此外，