论文标题
hausdorff和在非Archimedean领域的自我诉讼的盒子维度
Hausdorff and box dimension of self-affine set in non-Archimedean field
论文作者
论文摘要
在本文中，我们考虑了本地紧凑的非Archimedean字段$ \ MATHBB {F} $中的启用迭代功能系统。我们在$ \ mathbb {f} $中建立了奇异价值组成的理论，并在$ \ mathbb {f}^n $中构建了自动疗法的box和hausdorff维度，这是对真实情况的Falconer结果的类比。结果的优势是，对于实际情况，这些规范严格小于$ \ frac {1} {2} $，对于真实情况而言，不需要对仿期转换的线性零件的规范进行其他假设。
In this paper we consider affine iterated function systems in locally compact non-Archimedean field $\mathbb{F}$. We establish the theory of singular value composition in $\mathbb{F}$ and compute box and Hausdorff dimension of self-affine set in $\mathbb{F}^n$, in generic sense, which is an analogy of Falconer's result for real case. The result has the advantage that no additional assumptions needed to be imposed on the norms of linear parts of affine transformation while such norms are strictly less than $\frac{1}{2}$ for real case, which benefits from the non-Archimedean metric on $\mathbb{F}$.
