Centers of planar generalized Abel equations

Llibre, Jaume; Valls, Clàudìa

doi:10.1016/j.jde.2019.11.046

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Introduction and Statement Of The Main Results1

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2020

2025

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Cited by 5 publications

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“…The situation will be more intricate, see e.g. [1,2,12,13,16,22]. The existence and regularity of first integrals of an analytic differential system are related to dynamics on algebraic, geometry and topology, see e.g.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

Regularity and convergence of local first integrals of analytic differential systems

Zhang

2020

Preprint

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Poincaré 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 ∞ 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.

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