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Relative Lyapunov Centre Bifurcations

Wulff, C (2014) Relative Lyapunov Centre Bifurcations SIAM J. Applied Dynamical Systems, 13 (2). pp. 722-757.

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Relative equilibria and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur for example in celestial mechanics, molecular dynamics and rigid body motion. Relative equilibria are equilibria and RPOs are periodic orbits in the symmetry reduced system. Relative Lyapunov centre bifurcations are bifurcations of relative periodic orbits from relative equilibria corresponding to Lyapunov centre bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov centre theorem by combining recent results on persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov centre theorem of Montaldi et al. We then develop numerical methods for the detection of relative Lyapunov centre bifurcations along branches of RPOs and for their computation. We apply our methods to Lagrangian relative equilibria of the N body problem.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors : Wulff, C
Date : 2014
DOI : 10.1137/130925281
Related URLs :
Additional Information : Copyright: Society for Industrial and Applied Mathematics 2014
Depositing User : Symplectic Elements
Date Deposited : 13 Nov 2014 09:20
Last Modified : 29 Aug 2019 12:52

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