2013
DOI: 10.1088/0951-7715/26/10/2809
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Volume-preserving normal forms of Hopf-zero singularity

Abstract: A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-preserving classical normal forms of this singularity is introduced via a Lie algebra description. This is a maximal vector space of classical normal forms with first integral; this is whence our approach works. Systems with a non-zero condition on their quadratic parts are considered. The algebra of all first integrals for any such s… Show more

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Cited by 16 publications
(30 citation statements)
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“…A direct calculation using the Hamiltonian function given by the first item and Poisson bracket given by (2.8) establish (2.9) (see also preface of [13]). The last claim follows from the straightforward calculation of structure constants given by (2.8) and [16,Lemma 2.5].…”
Section: (P {· ·})mentioning
confidence: 97%
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“…A direct calculation using the Hamiltonian function given by the first item and Poisson bracket given by (2.8) establish (2.9) (see also preface of [13]). The last claim follows from the straightforward calculation of structure constants given by (2.8) and [16,Lemma 2.5].…”
Section: (P {· ·})mentioning
confidence: 97%
“…Similar to [16], one can remove Θ 0 0 using the linear change of variables, for further details, see [27,Lemma 5.3.6] and [17]. In what follows, we intend to simplify the second level normal form; w (2) .…”
Section: Normal Formmentioning
confidence: 99%
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