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In this paper, by using the method of Picard-Fuchs equation and Riccati equation, we study the upper bounds for the associated number of zeros of Abelian integrals for two classes… Click to show full abstract
In this paper, by using the method of Picard-Fuchs equation and Riccati equation, we study the upper bounds for the associated number of zeros of Abelian integrals for two classes of quadratic reversible centers of genus one under any polynomial perturbations of degree n, and obtain that their upper bounds are 3n− 3 (n ≥ 2) and 18 [ n 2 ] + 3 [ n−1 2 ] (n ≥ 4) respectively, both of the two upper bounds linearly depend on n.
Keywords:
zeros abelian;
abelian integrals;
upper bounds;
associated number;
number zeros;
bounds associated
Journal Title: Journal of Applied Analysis and Computation
Year Published: 2018
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Journal Title: Journal of Applied Analysis and Computation
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!