High order Melnikov method: Theory and application

Fengjuan Chen,Qiudong Wang

doi:10.1016/j.jde.2019.02.003

High order Melnikov method: Theory and application

Fengjuan Chen, Qiudong Wang

Open Access

https://doi.org/10.1016/j.jde.2019.02.003

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Journal: Journal of Differential Equations	Publication Date: Feb 14, 2019
Citations: 5	License type: publisher-specific-oa

Affiliation: Zhejiang Normal University, University of Arizona

#Formal Power Series #Order Equation + Show 8 more

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Abstract

Let D(t0,ε) be the splitting distance of the stable and unstable manifold of a time-periodic second order equation. We expand D(t0,ε) as a formal power series in ε asD(t0,ε)=E0(t0)+εE1(t0)+⋯+εnEn(t0)+⋯. In this paper we derive an explicit integral formula for E1(t0). We also evaluate E1(t0) to prove the existence of homoclinic tangles for an equation to which the Poincaré/Melnikov method fails to apply.

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