论文标题
方形矩阵的乘法和加性化合物的概括和Hausdorff尺寸的收缩
Generalization of the multiplicative and additive compounds of square matrices and contraction in the Hausdorff dimension
论文作者
论文摘要
矩阵的$ k $乘法和$ k $添加剂在几何形状，多线性代数，非线性动力学系统的渐近分析以及界限分形集的霍斯多夫维度方面起着重要作用。这些化合物定义为$ k $的整数值。在这里，我们介绍了称为$α$乘法和$α$添加化合物的概括，具有$α$真实。我们研究了这些新化合物的特性，并在Douady和Oesterlé定理的背景下演示了应用。这导致将合同系统概括为$α$承包系统，并具有$α$真实。粗略地说，此类系统的动态与大于$α$的Hausdorff尺寸设置的任何设置。对于$α= 1 $，它们将减少到标准承包系统。
The $k$ multiplicative and $k$ additive compounds of a matrix play an important role in geometry, multi-linear algebra, the asymptotic analysis of nonlinear dynamical systems, and in bounding the Hausdorff dimension of fractal sets. These compounds are defined for integer values of $k$. Here, we introduce generalizations called the $α$ multiplicative and $α$ additive compounds of a square matrix, with $α$ real. We study the properties of these new compounds and demonstrate an application in the context of the Douady and Oesterlé Theorem. This leads to a generalization of contracting systems to $α$ contracting systems, with $α$ real. Roughly speaking, the dynamics of such systems contracts any set with Hausdorff dimension larger than $α$. For $α=1$ they reduce to standard contracting systems.
