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

University of Groningen

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

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 - 1 Aug 2019

Keywords

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

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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 {\textquoteleft}generic{\textquoteright} bifurcations of structure-less {\textquoteleft}dissipative{\textquoteright} vector fields, up to a dimension-threshold that grows with the co-dimension of the bifurcation.",

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

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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 - Divergence-free vector field

KW - Double Hopf bifurcation

KW - KAM theory

KW - Quasi-periodic stability

KW - Volume-preserving Hopf bifurcation

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DO - 10.1007/s10440-019-00254-4

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Bifurcations in Volume-Preserving Systems

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Keywords

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