Perturbation theory for approximation of Lyapunov exponents by QR methods

被引：31

作者：

Dieci, Luca ^{[1
]}

Van Vleck, Erik S.

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2006年 / 18卷 / 03期

关键词：

Lyapunov exponents; integral separation; QR methods;

D O I：

10.1007/s10884-006-9024-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Motivated by a recently developed backward error analysis for QR methods, we consider the error in the Lyapunov exponents of perturbed triangular systems. We consider the case of stable and distinct Lyapunov exponents as well as the case of stable but not necessarily distinct exponents. We illustrate our analytical results with a numerical example.

引用

页码：815 / 840

页数：26

共 21 条

[1] ADRIANOVA LY, 1995, T MATH MONOGRAPHS AM, V146
[2] ARNOLD L, 1991, LECT NOTES MATH, V1486
[3] Arnold L., 1986, LECT NOTES MATH, V1186
[4] Benettin G, 1980, MECCANICA, V15, P21
[5] Bylov B. F., 1966, THEORY LYAPUNOV EXPO
[6] Bylov B. F., 1969, DIFF EQUAT+, V5, P1794
[7] GLOBAL LYAPUNOV EXPONENTS, KAPLAN-YORKE FORMULAS AND THE DIMENSION OF THE ATTRACTORS FOR 2D NAVIER-STOKES EQUATIONS
CONSTANTIN, P
FOIAS, C
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1985, 38 (01) : 1 - 27
[8] On the error in computing Lyapunov exponents by QR Methods
Dieci, L
Van Vleck, ES
[J]. NUMERISCHE MATHEMATIK, 2005, 101 (04) : 619 - 642
[9] On the computation of Lyapunov exponents for continuous dynamical systems
Dieci, L
Russell, RD
VanVleck, ES
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (01) : 402 - 423
[10] Lyapunov spectral intervals: Theory and computation
Dieci, L
Van Vleck, ES
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 40 (02) : 516 - 542

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