非自治康托集上调和测度的维数
Dimensions of harmonic measures on non-autonomous Cantor sets
AI总结：
该研究针对非自治共形迭代函数系的调和测度维数问题，发展非自治热力学形式工具，证明其豪斯多夫与填充维数的扰动连续性及满足Bowen、Manning型公式，补充了符号空间测度与正泛函的一般性结论。
摘要：
我们研究非自治共形迭代函数系（Non Autonomous Conformal Iterative Function Systems, NACIFS）及其极限集，核心关注调和测度的豪斯多夫维数与填充维数。我们证明这两个维数在扰动下具有连续性，且满足Bowen型与Manning型公式。为此，我们通过在非自治框架下发展热力学形式的工具，证明了符号空间上测度乃至更一般正泛函的相关一般性结果。
英文摘要：
We consider Non Autonomous Conformal Iterative Function Systems (NACIFS) and their limit set. Our main concern is harmonic measure and its dimensions : Hausdorff and Packing. We prove that this two dimensions are continuous under perturbations and that they verify Bowen's and Manning's type formulas. In order to do so we prove general results about measures, and more generally about positive functionals, defined on a symbolic space, developing tools from thermodynamical formalism in a non-autonomous setting.
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