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An integral representation for topological pressure in terms of conditional probabilities

机译:用条件概率表示拓扑压力的整数

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摘要

Given an equilibrium state A mu for a continuous function f on a shift of finite type X, the pressure of f is the integral, with respect to A mu, of the sum of f and the information function of A mu. We show that under certain assumptions on f, X and an invariant measure nu, the pressure of f can also be represented as the integral with respect to nu of the same integrand. Under stronger hypotheses we show that this representation holds for all invariant measures nu. We establish an algorithmic implication for approximation of pressure, and we relate our results to a result in thermodynamic formalism.
机译:给定一个连续函数f在有限类型X上的平衡状态A mu,相对于A mu,f的压力是f之和与A mu的信息函数的积分。我们表明,在关于f,X和不变度量nu的某些假设下,f的压力也可以表示为相对于同一被积数nu的积分。在更强的假设下,我们证明了这种表示适用于所有不变测度nu。我们建立了近似压力的算法含义,并将我们的结果与热力学形式主义的结果​​联系起来。

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