The University of Southampton
University of Southampton Institutional Repository

# Generic multiparameter bifurcation from a manifold

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

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.

Full text not available from this repository.

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

## Catalogue record

Date deposited: 20 Jul 2006