Bifurcations of the Polycycle “Tears of the Heart”: Multiple Numerical Invariants

IF 0.6 4区数学 Q3 MATHEMATICS

Moscow Mathematical Journal Pub Date : 2018-08-22 DOI:10.17323/1609-4514-2020-2-323-341

N. Goncharuk, Yury Kudryashov

引用次数: 4

Abstract

"Tears of the heart" is a hyperbolic polycycle formed by three separatrix connections of two saddles. It is met in generic 3-parameter families of planar vector fields. In [arXiv:1506.06797], it was discovered that generically, the bifurcation of a vector field with "tears of the heart" is structurally unstable. The authors proved that the classification of such bifurcations has a numerical invariant. In this article, we study the bifurcations of "tears of the heart" in more detail, and find out that the classification of such bifurcation may have arbitrarily many numerical invariants.

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多周期“心之泪”的分岔：多重数值不变量

“心之泪”是由两个鞍的三个分离线连接形成的双曲多环。它在平面向量场的一般3参数族中得到满足。在[arXiv:150606797]中，人们发现，一般来说，具有“心之泪”的向量场的分叉在结构上是不稳定的。作者证明了这类分叉的分类具有数值不变量。在本文中，我们更详细地研究了“心之泪”的分叉，并发现这种分叉的分类可能具有任意多个数值不变量。

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.