Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.02145 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In this paper, we explicitly obtain inhomogeneous Picard-Fuchs equations for Abelian integrals $I_{i,j}^+(h)$, where $I_{i,j}^+(h)$ is an integral along orbital arcs defined by polynomials $\frac{1}{2}y^2 + F(x)=h$. Moreover, we discuss the method of using Picard-Fuchs equations to recursively compute the asymptotic expansions of genearating functions of Abelian integrals near a homoclinic loop. As an application, we derive the maximum number of isolated zeros of Melnikov functions near a nilpotent saddle homoclinic loop for piecewise polynomials perturbations with the inclination $θ$ of the separation line as a free parameter.