On the Exponents of Exponential Dichotomies

被引：0
|
作者：
Battelli, Flaviano [1 ]
Feckan, Michal [2 ,3 ]
机构：
[1] Marche Polytecn Univ, Dept Ind Engn & Math, Ancona 60121, Italy
[2] Comenius Univ, Fac Math Phys & Informat, Dept Math Anal & Numer Math, Bratislava 84248, Slovakia
[3] Slovak Acad Sci, Math Inst, Stefanikova 49, Bratislava 81473, Slovakia
来源：
MATHEMATICS | 2020年 / 8卷 / 04期
关键词：
exponential dichotomy; roughness; asymptotically constant matrices; LINEAR-SYSTEMS; SEPARATION;
D O I：
10.3390/math8040651
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An exponential dichotomy is studied for linear differential equations. A constructive method is presented to derive a roughness result for perturbations giving exponents of the dichotomy as well as an estimate of the norm of the difference between the corresponding two dichotomy projections. This roughness result is crucial in developing a Melnikov bifurcation method for either discontinuous or implicit perturbed nonlinear differential equations.
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页数：13
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