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.
引用
收藏
页数：13
相关论文
共 50 条
  • [1] Tempered exponential dichotomies and Lyapunov exponents for perturbations
    Barreira, Luis
    Dragicevic, Davor
    Valls, Claudia
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2016, 18 (05)
  • [2] ON THE ROBUSTNESS OF EXPONENTIAL DICHOTOMIES
    Barreira, Luis
    Valls, Claudia
    FIXED POINT THEORY, 2015, 16 (01): : 31 - 47
  • [3] SMOOTH ROBUSTNESS OF EXPONENTIAL DICHOTOMIES
    Barreira, Luis
    Valls, Claudia
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 139 (03) : 999 - 1012
  • [4] Admissibility for exponential dichotomies in average
    Barreira, Luis
    Dragicevic, Davor
    Valls, Claudia
    STOCHASTICS AND DYNAMICS, 2015, 15 (03)
  • [5] Lyapunov sequences for exponential dichotomies
    Barreira, Luis
    Valls, Claudia
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 246 (01) : 183 - 215
  • [6] Characterization of strong exponential dichotomies
    Barreira, Luis
    Dragicevic, Davor
    Valls, Claudia
    BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2015, 46 (01): : 81 - 103
  • [7] Admissibility and nonuniform exponential dichotomies
    Dragicevic, Davor
    Zhang, Weinian
    Zhou, Linfeng
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 326 : 201 - 226
  • [8] EXPONENTIAL DICHOTOMIES AND FREDHOLM OPERATORS
    PALMER, KJ
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 104 (01) : 149 - 156
  • [9] Robustness of exponential dichotomies in mean
    Barreira, Luis
    Valls, Claudia
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2014, 124 (12) : 4244 - 4265
  • [10] Robustness of exponential dichotomies in mean
    Barreira, Luis, 1600, Elsevier B.V., Netherlands (124):
12345