The Number of Zeros of Abelian Integral for a Quintic Hamiltonian Systems With a Rose-Figure Loop

Abstract

Abstract In this article, we consider the near-Hamiltonian system where a < 0, 0 < |ε| << 1, f (x, y) and g(x, y) are polynomials of degree n ( n = 2 m , m ≥ 3, m ∈ N ). The number of isolated zeros of the corresponding Abelian integral for h ∈ is estimated.