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Generic multiparameter bifurcation from a manifold

Generic multiparameter bifurcation from a manifold
Generic multiparameter bifurcation from a manifold
The geometry of generic $k$-parameter bifurcation from an $n$-manifold is discussed for all values of $k,n$ with particular emphasis on the case $n=2$ (the case $n=1$ being dealt with in earlier work). Such bifurcations typically arise in the study of equilibrium states of dynamical systems with continuous (for example, spherical or toroidal) symmetry which undergo small symmetry-breaking perturbations, and in the use of Melnikov maps for detecting bifurcations of periodic orbits from resonance. Detailed analysis is given in the interesting case $n=2$, $k=3$ where the local geometry partly resembles unfolding of a degenerate wavefront or Legendrian collapse.
0268-1110
101-137
Chillingworth, D.R.J.
39d011b7-db33-4d7d-8dc7-c5a4e0a61231
Chillingworth, D.R.J.
39d011b7-db33-4d7d-8dc7-c5a4e0a61231

Chillingworth, D.R.J. (2000) Generic multiparameter bifurcation from a manifold. Dynamics and Stability of Systems, 15 (2), 101-137. (doi:10.1080/02681110050032119).

Record type: Article

Abstract

The geometry of generic $k$-parameter bifurcation from an $n$-manifold is discussed for all values of $k,n$ with particular emphasis on the case $n=2$ (the case $n=1$ being dealt with in earlier work). Such bifurcations typically arise in the study of equilibrium states of dynamical systems with continuous (for example, spherical or toroidal) symmetry which undergo small symmetry-breaking perturbations, and in the use of Melnikov maps for detecting bifurcations of periodic orbits from resonance. Detailed analysis is given in the interesting case $n=2$, $k=3$ where the local geometry partly resembles unfolding of a degenerate wavefront or Legendrian collapse.

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Published date: 2000

Identifiers

Local EPrints ID: 29793
URI: http://eprints.soton.ac.uk/id/eprint/29793
ISSN: 0268-1110
PURE UUID: edc7e6bc-70b4-4298-93e2-991496a78184

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Date deposited: 20 Jul 2006
Last modified: 15 Jul 2019 19:08

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