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| Paper IPM / M / 17635 |
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| Abstract: | |
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In this paper, we explore hypernormal forms of vector fields that have non-resonant double Hopf
singularities with a non-zero radial cubic part. Our primary focus is on investigating the infinite-level
normal form classification of this type of singularities. We provide a normal form decomposition in
terms of planar-rotating and planar-radial vector fields, which greatly facilitate the pattern recognition
and analysis of the corresponding generalized homological maps. Notably, our paper represents the
first instance of the normal form classification for general non-resonant double Hopf singularities
without structural symmetry.
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