Bifurcation and symmetry breaking

DOI10.1016/0370-1573(90)90168-2zbMath1211.58004OpenAlexW2092446028MaRDI QIDQ535915

Giuseppe Gaeta

Publication date: 15 May 2011

Published in: Physics Reports (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0370-1573(90)90168-2

Mathematics Subject Classification ID

Symmetry breaking in quantum theory (81R40) Phase transitions (general) in equilibrium statistical mechanics (82B26) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Group-invariant bifurcation theory in infinite-dimensional spaces (58E09)

Related Items (13)

Critical sections of gauge functionals: A symmetry approach ⋮ Lie-point symmetries and nonlinear dynamical systems ⋮ Counting symmetry-breaking solutions to symmetric variational problems ⋮ BREAKING OF LINEAR SYMMETRIES AND MICHEL'S THEORY: GRASSMANN MANIFOLDS, AND INVARIANT SUBSPACES ⋮ Autonomous systems, dynamical systems, LPTI symmetries, topology of trajectories, and periodic solutions ⋮ Symmetry-breaking bifurcations on multidimensional fixed point subspaces ⋮ Unnamed Item ⋮ Michel theory of symmetry breaking and gauge theories ⋮ Pseudo-spontaneous U(1) Symmetry breaking in hydrodynamics and holography ⋮ Nonclassical symmetry reductions of the Boussinesq equation ⋮ Breaking of permutation symmetry and diagonal group action: Nielsen model and the standard model as low-energy limit ⋮ Coupled nonlinear oscillators and the symmetries of animal gaits ⋮ Bifurcations, symmetries and the notion of fixed subspace

Cites Work

• Group theoretic methods in bifurcation theory. With an appendix by P. Olver
• Group representation theory, bifurcation theory and pattern formation
• On the structure of solutions of an equation in catalysis theory when a parameter is large
• The geometry of spontaneous symmetry breaking
• Numerical methods for bifurcation problems. Proceedings of the Conference at the University of Dortmund, August 22-26, 1983
• Symmetry and bifurcation in three-dimensional elasticity. II
• Nonlinear equations with superposition principles and the theory of transitive primitive Lie algebras
• A Poincaré-Bendixson theorem for scalar reaction diffusion equations
• Bifurcation of periodic solutions in a laser with saturable absorber
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Equivariant isotopies of semifree G-manifolds
• Pattern selection with \(\mathrm{O}(3)\) symmetry
• Lie groups and algebras with applications to physics, geometry, and mechanics
• Symmetries and pattern selection in Rayleigh-Bénard convection
• Singularities and groups in bifurcation theory. Volume I
• Generic bifurcation of Hamiltonian systems with symmetry. With an appendix by Jerrold Marsden
• Symmetry-breaking at positive solutions
• Symmetry-breaking for positive solutions of semilinear elliptic equations
• Bifurcation: analysis, algorithms, applications. Proceedings of the Conference at the University of Dortmund, August 18-22, 1986
• A classification of degenerate Hopf bifurcations with O(2) symmetry
• Pattern selection in ferrofluids
• Degenerate Hopf bifurcation in the presence of symmetry
• The physics of structure formation. Theory and simulation. Proceedings of an International Symposium, Tübingen, FRG, October 27 - November 2, 1986
• Pattern formation and bistability in flow between counterrotating cylinders
• Bifurcation with two parameters in two-dimensional complex space. Applications to laser systems
• Applications of centre manifold theory
• Imperfect bifurcation in the presence of symmetry
• Bifurcation from rotating waves
• Global bifurcation of periodic solutions with symmetry
• Singularities and groups in bifurcation theory. Volume II
• Smooth functions invariant under the action of a compact Lie group
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• The Hopf bifurcation theorem in infinite dimensions
• Hopf bifurcation at multiple eigenvalues
• Symmetry breaking and the maximal isotropy subgroup conjecture for reflection groups
• Symmetry and bifurcation in three-dimensional elasticity. I
• Bifurcation, perturbation of simple eigenvalues, and linearized stability
• Limit cycles with stability of the first level
• Bifurcation from simple eigenvalues
• Bifurcations in the presence of a symmetry group
• Transformation groups of spheres
• Gradient property of bifurcation equation for systems with rotational symmetry
• Hopf bifurcation with non-semisimple 1:1 resonance
• The G-invariant implicit function theorem in infinite dimensions
• Classification of systems of nonlinear ordinary differential equations with superposition principles
• Multiparameter Bifurcation Theory
• The G-invariant implicit function theorem in infinite dimensions II
• Symmetry and Stability in Taylor-Couette Flow
• Bifurcation on the hexagonal lattice and the planar Bénard problem
• Hopf bifurcation with the symmetry of the square
• Steady-state mode interactions in the presence of 0(2)-symmetry
• Stability of periodic solutions in symmetric Hopf bifurcation
• Periodic solutions near equilibria of symmetric Hamiltonian systems
• On degenerate Hopf bifurcation with broken O(2) symmetry
• On the existence of bifurcating solutions in the presence of symmetries
• Bifurcation and Stability of Convective Flows in a Rotating or not Rotating Spherical Shell
• Equivariant Dynamical Systems
• Bifurcation and symmetry breaking in applied mathematics
• Bifurcations withO(3) symmetry including applications to the Bénard problem
• Patterns of convection in spherical shells
• New algorithms for the Molien function
• Stratifications of equivariant varieties
• Group Representation Theory and Branch Points of Nonlinear Functional Equations
• A theory for imperfect bifurcation via singularity theory
• Patterns of convection in spherical shells. Part 2
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
• Hopf bifurcation in the presence of symmetry
• Quaternionic-like bifurcation in the absence of symmetry
• Quaternionic-like bifurcation in the absence of symmetry
• Vector fields on spheres
• Invariant manifolds
• Vector fields on spheres
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Bifurcation and symmetry breaking