Center conditions: Pull-back of differential equations

Zare, Yadollah

doi:10.1090/tran/7660

Center conditions: Pull-back of differential equations
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by Yadollah Zare PDF

Trans. Amer. Math. Soc. 372 (2019), 3167-3189 Request permission

Abstract:

The space of polynomial differential equations of a fixed degree with a center singularity has many irreducible components. We prove that pull-back differential equations form an irreducible component of such a space. The method used in this article is inspired by Ilyashenko and Movasati’s method. The main concepts are the Picard-Lefschetz theory of a polynomial in two variables with complex coefficients, the Dynkin diagram of the polynomial, and the iterated integral.

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