Center conditions: Rigidity of logarithmic differential equations. (Q1424496)
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| Language | Label | Description | Also known as |
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| English | Center conditions: Rigidity of logarithmic differential equations. |
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Center conditions: Rigidity of logarithmic differential equations. (English)
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14 March 2004
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The author shows that any degree \(d\) deformation of a generic logarithmic polynomial differential equation with a persistent center must be logarithmic also, thus generalizing Ilyashenko's result on Hamiltonian equations. Some applications are also given. A hint towards studying some of the notions presented here to the case of an algebraically closed field instead of \(\mathbb {C}\) is also presented.
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center conditions
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logarithmic differential equations
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rigidity
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holomorphic foliations
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Picard-Lefschetz theory
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