科研之友
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摘要
Suppose that the real generic cubic Hamiltonian H(x, y), (x, y) is an element of R(2), possesses three saddle points and one centre. Let Sigma subset of R be the set of values h of H(x, y), for which there exists a closed component delta(h) of the level curve {H(x, y) = h}, free of critical points. In this paper, we obtain a better upper bound than previously known for the number of zeros of the Abelian integrals I (h) = integral(delta(h))[g(x, y) dx - f (x, y) dy] for h is an element of Sigma in terms of the maximum of the degrees of the polynomials f (x, y) and g(x, y).
- 出版日期2010-12
