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Zeros of abelian integrals for the reversible codimension four quadratic centersQ r3 ∩Q 4

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Abstract

We study the number of zeros of Abelian integrals for the reversible codimension four quadratic centersQ R3 ∩Q 4, when we perturb such systems inside the class of all polynomial systems of degreen.

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Authors and Affiliations

  1. Department of Mathematics, Sun Yat-sen University, 510275, Guangzhou, People’s Republic of China

    Yulin Zhao

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  1. Yulin Zhao
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Correspondence to Yulin Zhao.

Additional information

Supported by grants from NSF of China (No. 10101031), Guangdong Natural Science Foundation (No. 001289), and NSF of Sun Yat-sen University for younger teachers.

The author wishes to thank Prof. R. Conti and Prof. G. Villari for their discussions, and Dipartimento di Matematica “U. Dini”, Università Degli Studi di Firenze for its support and hospitality during the period when this paper was elaborated. Y. Zhao is grateful to the referee for helpful suggestions.

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Zhao, Y. Zeros of abelian integrals for the reversible codimension four quadratic centersQ r3 ∩Q 4 . Isr. J. Math. 136, 125–143 (2003). https://doi.org/10.1007/BF02807194

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  • DOI: https://doi.org/10.1007/BF02807194

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