The Proof of Structural Stability of Hyperbolic Fixed Points in Ordinary Di®erential Equations

WANG Qi, ZHANG Shuo

doi:10.13371/j.cnki.chin.q.j.m.2018.01.011

Chinese Quarterly Journal of Mathematics >

2018 , Vol. 33 >Issue 1: 93 - 97

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2018.01.011

The Proof of Structural Stability of Hyperbolic Fixed Points in Ordinary Di®erential Equations

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School of Mathematics and Statistics Henan University

Wang Qi(1982-), male, native of Luoyang, Henan, associate professor of Henan University, Ph.D., engages in nonlinear functional analysisvariotianal methods; Zhang Shuo(1992-), female, native of Puyang,Henan, graduate student of Henan University, engages in nonlinear functional analysisvariotianal methods.

Accepted date: 2017-05-29

Online published: 2020-10-19

Supported by

Supported by NNSF of China(11301148)；

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Abstract

In ordinary differential equations, structural stability of hyperbolic fixed points is a classical result, but the proof of this result in [2] has same small mistake. In this paper,we will correct the above mistake by using the Hartman theorem and its idea.

Key words： Nonlinear system; Hyperbolic fixed point; Structural stability

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WANG Qi, ZHANG Shuo . The Proof of Structural Stability of Hyperbolic Fixed Points in Ordinary Di®erential Equations[J]. Chinese Quarterly Journal of Mathematics, 2018 , 33(1) : 93 -97 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.01.011

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