Global bifurcations in the two-sphere: a new perspective
成果类型：
Article
署名作者：
Ilyashenko, Yu.; Kudryashov, Yu.; Schurov, I.
署名单位：
HSE University (National Research University Higher School of Economics); Cornell University
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-018-0793-1
发表日期：
2018
页码：
461-506
关键词：
摘要：
We construct an open set of structurally unstable three parameter families whose weak and so called moderate topological classification defined below has a numerical invariant that may take an arbitrary positive value. Here and below families are families of vector fields in the two-sphere. This result disproves an Arnold's conjecture of 1985. Then we construct an open set of six parameter families whose moderate topological classification has a functional invariant. This invariant is an arbitrary germ of a smooth map . More generally, for any positive integers d and , we construct an open set of families whose topological classification has a germ of a smooth map as an invariant. Any smooth germ of this kind may be realized as such an invariant. These results open a new perspective of the global bifurcation theory in the two sphere. This perspective is discussed at the end of the paper.
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