Further elements on hypernormal forms of non-resonant double Hopf singularities

TL;DR

This paper classifies hypernormal forms of non-resonant double Hopf singularities, providing a decomposition approach that advances understanding of their structure without relying on symmetry assumptions.

Contribution

It introduces the first normal form classification for generic non-resonant double Hopf singularities lacking structural symmetry.

Findings

Normal form decomposition into planar-rotating and planar-radial vector fields

Facilitates pattern recognition in homological maps

First classification for non-resonant double Hopf singularities without symmetry

Abstract

In this paper, we deal with hypernormal forms of non-resonant double Hopf singularities. We investigate the infinite level normal form classification of such singularities with nonzero radial cubic part. We provide a normal form decomposition of normal form vector fields in terms of planar-rotating and planar-radial vector fields. These facilitate the pattern recognition and analysis of the corresponding generalized homological maps. This paper is the first instance of the normal form classification for generic non-resonant double Hopf singularities without structural symmetry.