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- W2354080778 abstract "V.I.Arnold posed the following problem several times:for given integers n≥2 and m≥3,what is the maximum number Z(m,n) of isolated zeros of the Abelian integrals of all polynomial 1-forms of degree n along all possible families of closed algebraic curves of degree m? We know from the Poincare-Pontryagin Theorem that,if the Abelian integral is not identically equal to zero,then A(n) = Z(n +1,n) gives the maximal number of limit cycles bifurcated from the periodic annuli of all Hamiltonian systems of degree n under any polynomial perturbations of degree n.Hence,Arnold named this problem the weakened 16th problem of Hilbert.During the past 30 years there was some progress on the research of this problem,but it is still quite far to solve it completely.In this paper we give a brief introduction of the problem and some relative research works." @default.
- W2354080778 created "2016-06-24" @default.
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- W2354080778 date "2010-01-01" @default.
- W2354080778 modified "2023-09-25" @default.
- W2354080778 title "Weak Hilbert's 16th Problem and the Relative Research" @default.
- W2354080778 hasPublicationYear "2010" @default.
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