TY - JOUR
T1 - High order Melnikov method
T2 - Theory and application
AU - Chen, Fengjuan
AU - Wang, Qiudong
N1 - Funding Information:
Research supported by National Nature Science Foundation of China (Nos. 11171309, 11471289).
Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/7/5
Y1 - 2019/7/5
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
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U2 - 10.1016/j.jde.2019.02.003
DO - 10.1016/j.jde.2019.02.003
M3 - Article
AN - SCOPUS:85061381971
SN - 0022-0396
VL - 267
SP - 1095
EP - 1128
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -