On the perron sign change effect for Lyapunov characteristic exponents of solutions of differential systems

被引：4
作者：
Korovin, S. K. [1 ]
Izobov, N. A.
机构：
[1] Moscow MV Lomonosov State Univ, Moscow, Russia
来源：
DIFFERENTIAL EQUATIONS | 2010年 / 46卷 / 10期
基金：
俄罗斯基础研究基金会;
关键词：
Lyapunov Exponent; Nontrivial Solution; Characteristic Exponent; Lyapunov Characteristic Exponent; Negative Lyapunov Exponent;
D O I：
10.1134/S0012266110100034
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Perron effect is the effect in which the characteristic Lyapunov exponents of solutions of a differential system change sign from negative to positive when passing to a perturbed system. We show that this effect is realized on all nontrivial solutions of two two-dimensional systems: an original linear system with negative characteristic exponents and a perturbed system with small perturbations of arbitrary order m > 1 in a neighborhood of the origin, all of whose nontrivial solutions have positive characteristic exponents. We compute the exact positive value of the characteristic exponents of solutions of the two-dimensional nonlinear Perron system with small second-order perturbations, which realizes only a partial Perron effect.
引用
收藏
页码：1395 / 1408
页数：14
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