Further study on Horozov-Iliev's method of estimating the number of limit cycles

TL;DR

This paper advances a method for estimating the maximum number of zeros of the Melnikov function, which is crucial for determining the number of limit cycles in near-Hamiltonian systems.

Contribution

It develops an improved technique to better estimate the upper bound of zeros of the Melnikov function in the context of limit cycle analysis.

Findings

Enhanced estimation method for zeros of Melnikov function

More accurate upper bounds for limit cycle count

Applicable to near-Hamiltonian systems

Abstract

In the study of the number of limit cycles of near-Hamiltonian systems, the first order Melnikov function plays an important role. This paper aims to establish a development of a known method to estimate the upper bound of the number of zeros of the function.