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- W1545552320 abstract "We explore the convergence/divergence of the normal form for a singularity of a vector field on $C^n$ with nilpotent linear part. We show that a Gevrey-$alpha$ vector field $X$ with a nilpotent linear part can be reduced to a normal form of Gevrey-$1+alpha$ type with the use of a Gevrey-$1+alpha$ transformation. We also give a proof of the existence of an optimal order to stop the normal form procedure. If one stops the normal form procedure at this order, the remainder becomes exponentially small." @default.
- W1545552320 created "2016-06-24" @default.
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- W1545552320 date "2011-10-17" @default.
- W1545552320 modified "2023-09-23" @default.
- W1545552320 title "Normal forms with exponentially small remainder and Gevrey normalization for vector fields with a nilpotent linear part" @default.
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- W1545552320 doi "https://doi.org/10.48550/arxiv.1110.3810" @default.
- W1545552320 hasPublicationYear "2011" @default.
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