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) |
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Pages (from-to) | 1095-1128 |
Number of pages | 34 |
Journal | Journal of Differential Equations |
Volume | 267 |
Issue number | 2 |
DOIs | |
State | Published - Jul 5 2019 |
Externally published | Yes |
Keywords
- High order Melnikov method
- Homoclinic intersection
- Time periodic equation
ASJC Scopus subject areas
- Analysis
- Applied Mathematics