NONUNIFORM DICHOTOMY SPECTRUM INTERVALS: THEOREM AND COMPUTATION

Hailong Zhu; Zhaoxiang Li

doi:10.11948/2156-907X.20180297

2019 Volume 9 Issue 3

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Hailong Zhu, Zhaoxiang Li. NONUNIFORM DICHOTOMY SPECTRUM INTERVALS: THEOREM AND COMPUTATION[J]. Journal of Applied Analysis & Computation, 2019, 9(3): 1102-1119. doi: 10.11948/2156-907X.20180297

Citation:

Hailong Zhu, Zhaoxiang Li. NONUNIFORM DICHOTOMY SPECTRUM INTERVALS: THEOREM AND COMPUTATION[J]. Journal of Applied Analysis & Computation, 2019, 9(3): 1102-1119. doi: 10.11948/2156-907X.20180297

NONUNIFORM DICHOTOMY SPECTRUM INTERVALS: THEOREM AND COMPUTATION

Hailong Zhu¹,
Zhaoxiang Li^2,3, ,

1.
School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, China
2.
Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China
3.
Department of Mathematics, Shanghai University, Shanghai, 200444, China

Corresponding author: Email address:zxli@shnu.edu.cn(Z. Li)
Fund Project: The first author was supported by the NSF of China (No. 11671118), China Postdoctoral Science Foundation funded project (No. 2016M591697), NSF of Anhui Province of China(No. gxfxZD2016090 and No. KJ2018A0437). The second author was supported by the NSF of China (No. 11871043, No. 11771298 and No. 11671251) and China Postdoctoral Science Foundation(No.2015M571538)

Abstract

Abstract

In this paper, on the condition of nonuniformly bounded growth, we give the relationship between the nonuniform exponential dichotomy spectrum and the other two classical spectrums (the Lyapunov spectrum and Sacker-Sell spectrum), present their stability under small linear perturbations. The main goal of this paper is to discuss the theory for the computation of these spectrums on the condition of nonuniformly bounded growth, and this extends the work of Dieci and Vleck [22], which computes the Lyapunov spectrum and Sacker-Sell spectrum under the condition of bounded. Finally, the numerical examples are given to illustrate and verify the theoretical results.
- Lyapunov exponents /
- nonuniform exponential dichotomy spectrum /
- spectrum Intervals /
- weak integral separation
MSC: 34D08, 34D09

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References

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