We provide an entirely new approach to the theory of thermodynamic formalism for entire functions of bounded type. The key point is that we introduce an integral means spectrum for logarithmic tracts which takes care of the fractal behavior of the boundary of the tract near infinity. It turns out that this spectrum behaves well as soon as the tracts have some sufficiently nice geometry which, for example, is the case for quasidisk, John or Hölder tracts. In these cases we get a good control of the corresponding transfer operators, leading to full thermodynamic formalism along with its applications such as exponential decay of correlations, central limit theorem and a Bowen’s formula for the Hausdorff dimension of radial Julia sets. This approach covers all entire functions for which thermodynamic formalism has been so far established and goes far beyond. It applies in particular to every hyperbolic function from any Eremenko-Lyubich analytic family of Speiser class S provided this family contains at least one function with Hölder tracts. The latter is, for example, the case if the family contains a Poincaré linearizer.

中文翻译：

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热力学形式主义和积分表示超越整函数的对数域谱

我们为有界类型的整个函数的热力学形式主义理论提供了一种全新的方法。关键是我们为对数束引入了一个积分均值谱，它处理了接近无穷大的束边界的分形行为。事实证明，只要区域具有足够好的几何形状，例如 quasidsk、John 或 Hölder 区域的情况，该谱就会表现良好。在这些情况下，我们可以很好地控制相应的传递算子，从而导致完整的热力学形式主义及其应用，例如相关性的指数衰减、中心极限定理和用于径向 Julia 集的 Hausdorff 维数的 Bowen 公式。这种方法涵盖了迄今为止热力学形式主义已经建立并远远超出的所有全部功能。它特别适用于来自 Speiser S 类的任何 Eremenko-Lyubich 分析族的每一个双曲线函数，前提是该族至少包含一个带有 Hölder 束的函数。例如，后者是该系列包含 Poincaré 线性化器的情况。