One of the most pressing problems in modern analysis is the study of the growth rate of the norms of all possible matrix products $\|A_{i_{n}}\cdots A_{i_{0}}\|$ with factors from a set of matrices $\mathscr{A}$. So far, only for a relatively small number of classes of matrices $\mathscr{A}$ has it been possible to rigorously describe the sequences of matrices $\{A_{i_{n}}\}$ that guarantee the maximal growth rate of the corresponding norms. Moreover, in almost all theoretically studied cases, the index sequences $\{i_{n}\}$ of matrices maximizing the norms of the corresponding matrix products turned out to be periodic or so-called Sturmian sequences, which entails a whole set of "good" properties of the sequences $\{A_{i_{n}}\}$, in particular the existence of a limiting frequency of occurrence of each matrix factor $A_{i}\in\mathscr{A}$ in them. The paper determines a class of $2\times 2$ matrices consisting of two matrices similar to rotations of the plane in which the sequence $\{A_{i_{n}}\}$ maximizing the growth rate of the norms $\|A_{i_{n}}\cdots A_{i_{0}}\|$ is not Sturmian. All considerations are based on numerical modeling and cannot be considered mathematically rigorous in this part. Rather, they should be interpreted as a set of questions for further comprehensive theoretical analysis.

翻译：现代分析中最紧迫的问题之一是研究所有可能的矩阵产品“A”和“A”和“A”的增长率。到目前为止,只有数量相对较少的“马斯克勒”和“A”类,才可能严格描述保证相应标准最大增长率的矩阵序列。此外,在几乎所有理论上研究的案例中,将相应的矩阵产品的全面规范最大化为定期或所谓的“Sturmian”序列的指数序列(美元)和“马”类相对较少的类别(美元)的指数序列(美元)和“美元”的指数序列(美元)的增长率。 本文确定了一种2倍的矩阵(美元),组成两个类似于“亚”和“美元”系列(美元)的模型(美元)的模型(美元)和“美元”数级(美元)的模型(美元)值(美元)值(美元)值(美元)值(美元)值(美元)值(美元)值(美元)的指数序列(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)(美元)