Reversible equivariant linear systems

DOI10.1006/jdeq.1999.3632zbMath0954.37016OpenAlexW2041926611MaRDI QIDQ1960915

Jeroen S. W. Lamb, Roberts, Mark

Publication date: 12 February 2001

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1999.3632

zbMATH Keywords

symmetrynormal formlocal bifurcationirreducible representation of compact Lie grouplinear time-reversal symmetryreversible equivariant linear system

Mathematics Subject Classification ID

Normal forms for dynamical systems (37G05) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40)

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Cites Work

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• Reversible systems
• Singularities and groups in bifurcation theory. Volume II
• Conjugacy classes in linear groups
• Local bifurcations on the plane with reversing point group symmetry
• Normal forms and unfoldings of linear systems in eigenspaces of (anti)-automorphisms of order two
• Versal deformations and normal forms for reversible and Hamiltonian linear systems
• Stability of Equilibria for a Class of Time-Reversible, $D_n \times O(2)$-Symmetric Homogeneous Vector Fields
• Periodic solutions near equilibria of symmetric Hamiltonian systems
• Reversing symmetries in dynamical systems
• Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group
• Versal unfoldings of equivariant linear Hamiltonian vector fields
• Time-Reversibility and Particle Sedimentation