Reverse算法的收敛性与组合结构
Convergence and combinatorics of the Reverse algorithm
AI总结：
研究非幺模的多维连分数Reverse算法的遍历性、指数收敛性，并证明其第二李雅普诺夫指数为负，进而分析由算法生成的S-adic语言的平衡性，给出具体平衡语言族。
摘要：
我们研究了Reverse算法，这是一种非幺模的多维连分数算法。我们证明了Reverse算法是遍历的，并通过证明其第二李雅普诺夫指数为负，表明该算法几乎处处指数收敛。此外，我们为该算法附加了替换规则，并研究了由这些替换序列生成的S-adic语言。第二李雅普诺夫指数的负性意味着几乎所有这类语言都是平衡的。通过对替换规则的组合结构进行深入研究，我们甚至能够获得一个具体的平衡语言族，该族通过底层替换序列上的简单条件来刻画。
英文摘要：
We study the Reverse algorithm, a multidimensional continued fraction algorithm, which is not unimodular. We show that the Reverse algorithm is ergodic and, by proving that its second Lyapunov exponent is negative, that it is a.e. exponentially convergent. In addition to that, we attach substitutions to this algorithm and study the $S$-adic languages generated by sequences of these substitutions. The negativity of the second Lyapunov exponent implies that almost all of these languages are balanced. By a thorough study of the combinatorics of the substitutions, we are even able to obtain a concrete generic family of balanced languages that is characterized in terms of a simple condition on the underlying sequence of substitutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
