Finite approximations of Frobenius-Perron operators. A solution of Ulam's conjecture to multi-dimensional transformations

被引：57

作者：

Ding, J ^{[1
]}

Zhou, AH ^{[1
]}

机构：

[1] ACAD SINICA,INST SYST SCI,BEIJING 100080,PEOPLES R CHINA

来源：

PHYSICA D | 1996年 / 92卷 / 1-2期

关键词：

Frobenius-Perron operators; invariant measures;

D O I：

10.1016/0167-2789(95)00292-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that Ulam's piecewise constant approximation algorithm is convergent for computing an absolutely continuous invariant measure associated with a piecewise C-2 expanding transformation or a Jablonski transformation S: [0, 1](N) C R(N) --> [0, 1](N). This solves an extension of Ulam's conjecture to multi-dimensions and generalizes the convergence result given by T.-Y. Li for one-dimensional transformations.

引用

页码：61 / 68

页数：8

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