论文标题
与全体形态数据相关的转移操作员的拉格朗日近似
Lagrange approximation of transfer operators associated with holomorphic data
论文作者
论文摘要
我们表明，可以使用基于Lagrange插值的有效数值方案来近似由Holomorthic Data给出的转移运算符的光谱数据。特别是，我们表明，对于满足某些复杂收缩特性的一维系统，近似值的光谱数据将指数收敛于转移运算符的光谱数据，并由基础系统的各个复杂收缩比确定的指数速率。我们通过从文献中提到的示例来证明了该方案的有效性，该方案通过数值计算由间隔和圆形图引起的转移操作员的特征值以及（正）随机矩阵产物和迭代功能系统的Lyapunov指数。
We show that spectral data of transfer operators given by holomorphic data can be approximated using an effective numerical scheme based on Lagrange interpolation. In particular, we show that for one-dimensional systems satisfying certain complex contraction properties, spectral data of the approximants converge exponentially to the spectral data of the transfer operator with the exponential rate determined by the respective complex contraction ratios of the underlying systems. We demonstrate the effectiveness of this scheme by numerically computing eigenvalues of transfer operators arising from interval and circle maps, as well as Lyapunov exponents of (positive) random matrix products and iterated function systems, based on examples taken from the literature.
