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- W3100887984 abstract "Poincar'e proved nonexistence of formal first integrals near a nonresonant singularity of analytic autonomous differential systems. In the resonant case with one zero eigenvalue and others nonresonant, there remains an open problem on regularity and convergence of local first integrals. Here we provide an answer to this problem. The system has always a local $C^infty$ first integral near the singularity when it is nonisolated. In any finite dimensional space formed by analytic differential systems having the same linear part at the singularity, either all the systems have local analytic first integrals or only the systems in a pluripolar subset have local analytic first integrals." @default.
- W3100887984 created "2020-11-23" @default.
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- W3100887984 date "2020-11-16" @default.
- W3100887984 modified "2023-09-23" @default.
- W3100887984 title "Regularity and convergence of local first integrals of analytic differential systems" @default.
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- W3100887984 doi "https://doi.org/10.48550/arxiv.2011.09309" @default.
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