Abstract
Let D(t 0 ,ε) be the splitting distance of the stable and unstable manifold of a time-periodic second order equation. We expand D(t 0 ,ε) as a formal power series in ε as D(t 0 ,ε)=E 0 (t 0 )+εE 1 (t 0 )+⋯+ε n E n (t 0 )+⋯. In this paper we derive an explicit integral formula for E 1 (t 0 ). We also evaluate E 1 (t 0 ) to prove the existence of homoclinic tangles for an equation to which the Poincaré/Melnikov method fails to apply.
Original language | English (US) |
---|---|
Journal | Journal of Differential Equations |
DOIs | |
State | Published - Jan 1 2019 |
Fingerprint
Keywords
- High order Melnikov method
- Homoclinic intersection
- Time periodic equation
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
Cite this
High order Melnikov method : Theory and application. / Chen, Fengjuan; Wang, Qiu-Dong.
In: Journal of Differential Equations, 01.01.2019.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - High order Melnikov method
T2 - Theory and application
AU - Chen, Fengjuan
AU - Wang, Qiu-Dong
PY - 2019/1/1
Y1 - 2019/1/1
N2 - Let D(t 0 ,ε) be the splitting distance of the stable and unstable manifold of a time-periodic second order equation. We expand D(t 0 ,ε) as a formal power series in ε as D(t 0 ,ε)=E 0 (t 0 )+εE 1 (t 0 )+⋯+ε n E n (t 0 )+⋯. In this paper we derive an explicit integral formula for E 1 (t 0 ). We also evaluate E 1 (t 0 ) to prove the existence of homoclinic tangles for an equation to which the Poincaré/Melnikov method fails to apply.
AB - Let D(t 0 ,ε) be the splitting distance of the stable and unstable manifold of a time-periodic second order equation. We expand D(t 0 ,ε) as a formal power series in ε as D(t 0 ,ε)=E 0 (t 0 )+εE 1 (t 0 )+⋯+ε n E n (t 0 )+⋯. In this paper we derive an explicit integral formula for E 1 (t 0 ). We also evaluate E 1 (t 0 ) to prove the existence of homoclinic tangles for an equation to which the Poincaré/Melnikov method fails to apply.
KW - High order Melnikov method
KW - Homoclinic intersection
KW - Time periodic equation
UR - http://www.scopus.com/inward/record.url?scp=85061381971&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85061381971&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2019.02.003
DO - 10.1016/j.jde.2019.02.003
M3 - Article
AN - SCOPUS:85061381971
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
ER -