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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Center conditions: Pull-back of differential equations


Author: Yadollah Zare
Journal: Trans. Amer. Math. Soc. 372 (2019), 3167-3189
MSC (2010): Primary 14P05, 32S65, 34C07, 37F75
DOI: https://doi.org/10.1090/tran/7660
Published electronically: June 6, 2019
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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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Additional Information

Yadollah Zare
Affiliation: Instituto Nacional de Matemática Pura e Aplicada-IMPA, Rio de Janeiro - RJ, 22460-320, Brazil
Email: yadollah2806@gmail.com, yadollah@impa.br

DOI: https://doi.org/10.1090/tran/7660
Keywords: Holomorphic foliations, Picard-Lefschetz theory
Received by editor(s): July 31, 2017
Received by editor(s) in revised form: April 5, 2018, May 2, 2018, and July 3, 2018
Published electronically: June 6, 2019
Dedicated: Dedicated to Hossein Movasati
Article copyright: © Copyright 2019 American Mathematical Society