A Generalization of the Gauss-Kuzmin-Wirsing constant

连分数Gauss问题的验证数值方法

Validated numerics for the Gauss problem on continued fractions

本文通过验证数值方法估计连分数中的Gauss-Kuzmin-Wirsing常数，给出其高精度数值界限。

关于最近整数连分数的Gauss-Kuzmin-Lévy问题

On the Gauss-Kuzmin-Lévy problem for nearest integer continued fractions

本文针对最近整数连分数相关的Gauss型移位，在区间 $I_0=[0,\frac{1}{2}]$ 或 $[-\frac{1}{2},\frac{1}{2}]$ 上证明了Gauss-Kuzmin-Lévy问题的有效渐近界，其中收敛速率 $q=0.288$ 优于Wirsing常数。

A gauss-kuzmin theorem and related questions for $θ$-expansions

Using the natural extension for $θ$-expansions, we give an infinite-order-chain representation of the sequence of the incomplete quotients of these expansions. Together with the ergodic behavior of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the above fraction expansion.

Ergodic Properties Of $θ$-Expansions And A Gauss-Kuzmin-Type Problem

A generalization of the regular continued fractions was given by Chakraborty and Rao \cite{CR-2003}. For the transformation which generates this expansion and its invariant measure, the Perron-Frobenius operator is given and studied. For this expansion, we apply the method of Rockett and Szüsz \cite{RS-1992} and obtained the solution of its Gauss-Kuzmin-type problem.

A Generalization of Gauss-Kuzmin-Lévy Theorem

We prove a generalized Gauss-Kuzmin-Lévy theorem for the $p$-numerated generalized Gauss transformation $$T_p(x)=\{\frac{p}{x}\}.$$ In addition, we give an estimate for the constant that appears in the theorem.

三维空间中克莱因帆的广义高斯-库兹明分布

Generalised Gauss--Kuzmin Distribution for Klein sails in $\mathbb R^3$

本文将经典高斯-库兹明分布推广至三维空间，证明一般克莱因帆局部面结构的等分布，解决Karpenkov公开问题，通过构造SL₃(ℝ)/SL₃(ℤ)对角流的有限截面测度推导极限面统计量。