Integrable Deformations of Foliations: a Generalization of Ilyashenko's Result

IF 0.6 4区数学 Q3 MATHEMATICS

Moscow Mathematical Journal Pub Date : 2018-11-10 DOI:10.17323/1609-4514-2021-21-2-271-286

D. Cerveau, B. Sc'ardua

引用次数: 2

Abstract

We study analytic deformations of holomorphic differential 1-forms. The initial 1-form is exact homogeneous and the deformation is by polynomial integrable 1-forms. We investigate under which conditions the elements of the deformation are still exact or, more generally, exhibit a first integral. Our results are related to natural extensions of classical results of Ilyashenko on limit cycles of perturbations of hamiltonian systems in two complex variables.

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叶形的可积变形:对Ilyashenko结果的推广

研究全纯微分1型的解析变形。初始1-形式是精确齐次的，变形是多项式可积的1-形式。我们研究在哪些条件下变形的元素仍然是精确的，或者更一般地说，表现出一个第一积分。我们的结果与Ilyashenko关于两个复变量哈密顿系统摄动极限环的经典结果的自然推广有关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Moscow Mathematical Journal 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular. An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.