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- Title
On the Algebraic Structure and the Number of Zeros of Abelian Integral for a Class of Hamiltonians with Degenerate Singularities.
- Authors
Yang, Jihua
- Abstract
The sixteen generators of Abelian integral I(h)=∮Γhg(x,y)dx-f(x,y)dy, which satisfy eight different Picard-Fuchs equations respectively, are obtained, where Γh is a family of closed orbits defined by H(x,y)=ax4+by4+cx8=h, h∈Σ, Σ is the open intervals on which Γh is defined, and f(x, y) and g(x, y) are real polynomials in x and y of degree n. Moreover, an upper bound of the number of zeros of I(h) is obtained for a special case f(x,y)=∑0≤i≤4k+1=naix4k+1-iyi,g(x,y)=∑0≤i≤4k+1=nbix4k+1-iyi.
- Subjects
ORDERED algebraic structures; HAMILTON'S principle function; MATHEMATICAL singularities; POLYNOMIALS; CHEBYSHEV approximation
- Publication
Bulletin of the Brazilian Mathematical Society, 2018, Vol 49, Issue 4, p893
- ISSN
1678-7544
- Publication type
Article
- DOI
10.1007/s00574-018-0085-9