Equivariant bifurcation theory and symmetry breaking

DOI10.1007/BF01048455zbMath0693.58014OpenAlexW2008909299MaRDI QIDQ908563

Mike Field

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1007/bf01048455

zbMATH Keywords

topological degreesymmetry breakingcompact Lie groupstratificationsdeterminacyequivariant bifurcation theoryequivariant dynamical systemsequivariant transversality

Mathematics Subject Classification ID

Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items

Heteroclinic cycles and wreath product symmetries, Stability of Cycles in a Game of Rock-Scissors-Paper-Lizard-Spock, Robust heteroclinic cycles, Onset of intermittent octahedral patterns in spherical Bénard convection, Symmetry breaking in equivariant bifurcation problems, Global planar dynamics with a star node and contracting nonlinearity, Patterns of desynchronization and resynchronization in heteroclinic networks, Attractor bifurcation of three-dimensional double-diffusive convection, Symmetry-breaking and branching patterns in equivariant bifurcation theory. I, Symmetry breaking and branching patterns in equivariant bifurcation theory. II, Heteroclinic cycles in dynamical systems with broken spherical symmetry, Bifurcation diagrams and heteroclinic networks of octagonal H-planforms, Heteroclinic cycles for reaction diffusion systems by forced symmetry-breaking, Symmetry-breaking bifurcations on multidimensional fixed point subspaces, Symmetry breaking and fractal dependence on initial conditions in dynamical systems: Ordinary differential equations of thermal convection, Steady-state bifurcation with O(3)-symmetry, Symmetry \& critical points for a model shallow neural network, Breaking of permutation symmetry and diagonal group action: Nielsen model and the standard model as low-energy limit, Equivariant bifurcation, quadratic equivariants, and symmetry breaking for the standard representation of S _k

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Minima of Higgs potentials corresponding to non-maximal isotropy subgroups
• Singularities and groups in bifurcation theory. Volume I
• A proof of the \(C^ 1\) stability conjecture
• An equivariant setting of the Morse theory
• Singularities and groups in bifurcation theory. Volume II
• Topological stability of smooth mappings
• Symmetry breaking and the maximal isotropy subgroup conjecture for reflection groups
• Structural stability of vector fields
• Equivariant differential topology
• Morse inequalities for a dynamical system
• Structurally stable heteroclinic cycles
• Topological equivalence of bifurcation problems
• Equivariant Dynamical Systems
• General Position of Equivariant Maps
• Transversality in G-Manifolds
• The Yang-Mills equations over Riemann surfaces
• Differentiable dynamical systems
• Hopf bifurcation in the presence of symmetry
• Invariant manifolds