Bifurcations in Volume-Preserving Systems

Henk W. Broer; Heinz Hanssmann

doi:10.1007/s10440-019-00254-4

Bifurcations in Volume-Preserving Systems

Henk W. Broer^*, Heinz Hanssmann

^*Corresponding author for this work

Dynamical Systems, Geometry and Mathematical Physics

Research output: Contribution to journal › Article › Academic › peer-review

2 Citations (Scopus)

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Abstract

We give a survey on local and semi-local bifurcations of divergence-free vector fields. These differ for low dimensions from generic' bifurcations of structure-less dissipative' vector fields, up to a dimension-threshold that grows with the co-dimension of the bifurcation.

Original language	English
Pages (from-to)	3-32
Number of pages	30
Journal	Acta applicandae mathematicae
Volume	162
Issue number	1
DOIs	https://doi.org/10.1007/s10440-019-00254-4
Publication status	Published - Aug-2019

Keywords

KAM theory
Divergence-free vector field
Volume-preserving Hopf bifurcation
Double Hopf bifurcation
Quasi-periodic stability
GAMES

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10.1007/s10440-019-00254-4Licence: CC BY

Bifurcations in Volume-Preserving SystemsFinal publisher's version, 952 KBLicence: CC BY

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title = "Bifurcations in Volume-Preserving Systems",

abstract = "We give a survey on local and semi-local bifurcations of divergence-free vector fields. These differ for low dimensions from generic' bifurcations of structure-less dissipative' vector fields, up to a dimension-threshold that grows with the co-dimension of the bifurcation.",

keywords = "KAM theory, Divergence-free vector field, Volume-preserving Hopf bifurcation, Double Hopf bifurcation, Quasi-periodic stability, GAMES",

author = "Broer, {Henk W.} and Heinz Hanssmann",

year = "2019",

month = aug,

doi = "10.1007/s10440-019-00254-4",

language = "English",

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AU - Broer, Henk W.

AU - Hanssmann, Heinz

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AB - We give a survey on local and semi-local bifurcations of divergence-free vector fields. These differ for low dimensions from generic' bifurcations of structure-less dissipative' vector fields, up to a dimension-threshold that grows with the co-dimension of the bifurcation.

KW - KAM theory

KW - Divergence-free vector field

KW - Volume-preserving Hopf bifurcation

KW - Double Hopf bifurcation

KW - Quasi-periodic stability

KW - GAMES

U2 - 10.1007/s10440-019-00254-4

DO - 10.1007/s10440-019-00254-4

M3 - Article

SN - 0167-8019

VL - 162

SP - 3

EP - 32

JO - Acta applicandae mathematicae

JF - Acta applicandae mathematicae

IS - 1

ER -

Bifurcations in Volume-Preserving Systems

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