Analytic enclosure of the fundamental matrix solution

被引：4

作者：

Castelli, Roberto ^{[1
]}

Lessard, Jean-Philippe ^{[2
]}

James, Jason D. Mireles ^{[3
]}

机构：

[1] Vrije Univ Amsterdam, Dept Math, Fac Sci, NL-1081 HV Amsterdam, Netherlands

[2] Univ Laval, Dept Math & Stat, Quebec City, PQ G1V 0A6, Canada

[3] Florida Atlantic Univ, Boca Raton, FL 33431 USA

来源：

APPLICATIONS OF MATHEMATICS | 2015年 / 60卷 / 06期

基金：

美国国家科学基金会;

关键词：

rigorous numerics; fundamental matrix solution; Floquet theory; analytical category; INVARIANT-MANIFOLDS; PARAMETERIZATION METHOD; PERIODIC-ORBITS; NUMERICS;

D O I：

10.1007/s10492-015-0114-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This work describes a method to rigorously compute the real Floquet normal form decomposition of the fundamental matrix solution of a system of linear ODEs having periodic coefficients. The Floquet normal form is validated in the space of analytic functions. The technique combines analytical estimates and rigorous numerical computations and no rigorous integration is needed. An application to the theory of dynamical system is presented, together with a comparison with the results obtained by computing the enclosure in the C (s) category.

引用

页码：617 / 636

页数：20

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