Nonuniform dichotomy spectrum and reducibility for nonautonomous difference equations-Reference-Cited by-同舟云学术

Nonuniform dichotomy spectrum and reducibility for nonautonomous difference equations

Published:2021-07-24 Issue:1 Volume:11 Page:369-384
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Chu Jifeng¹,Liao Fang-Fang¹,Siegmund Stefan²,Xia Yonghui³,Zhu Hailong⁴

Affiliation:

1. Department of Mathematics, Shanghai Normal University , Shanghai 200234 , China

2. Center for Dynamics & Institute of Analysis, Faculty of Mathematics , TU Dresden , Germany

3. School of Mathematics and Computer Science, Zhejiang Normal University , Jinhua , China

4. Anhui University of Finance and Economics , Bengbu 233030 , China

Abstract

Abstract For nonautonomous linear difference equations, we introduce the notion of the so-called nonuniform dichotomy spectrum and prove a spectral theorem. As an application of the spectral theorem, we prove a reducibility result.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Link

https://www.degruyter.com/document/doi/10.1515/anona-2020-0198/pdf

Reference35 articles.

1. B. Aulbach, The fundamental existence theorem on invariant fiber bundles, J. Difference Equ. Appl. 3 (1998), 267-312.

2. B. Aulbach, N. V. Minh, P. P. Zabreiko, The concept of spectral dichotomy for linear difference equations, J. Math. Anal. Appl. 185 (1994), 275-287.

3. B. Aulbach, N. V. Minh, The concept of spectral dichotomy for linear difference equations II, J. Difference Equ. Appl. 2 (1996), 251-262.

4. B. Aulbach, S. Siegmund, A spectral theory for nonautonomous difference equations, New trends in difference equations (Temuco, 2000), 45-55, Taylor & Francis, London, 2002.

5. L. Barreira, Ya. Pesin, Lyapunov Exponents and Smooth Ergodic Theory, University Lecture Series 23, Amer. Math. Soc. 2002.

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Normal Forms for Nonautonomous Nonlinear Difference Systems Under Nonuniform Dichotomy Spectrum;Journal of Function Spaces;2024-01

2. The Case of Differential Equations;SpringerBriefs in Mathematics;2023-12-14

3. Spectra and Examples;SpringerBriefs in Mathematics;2023-12-14

4. Nonuniform μ-dichotomy spectrum and kinematic similarity;Journal of Differential Equations;2023-12

5. Homoclinic Solutions for Partial Difference Equations with Mixed Nonlinearities;The Journal of Geometric Analysis;2023-02-02