A symmetry-breaking bifurcation theorem and some related theorems applicable to maps having unbounded derivatives

DOI10.1007/BF03167432zbMath1054.37030OpenAlexW4236855339MaRDI QIDQ1880945

Tadashi Kawanago

Publication date: 27 September 2004

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03167432

zbMATH Keywords

bifurcationsymmetry breaking

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Vibrations in dynamical problems in solid mechanics (74H45) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Abstract bifurcation theory involving nonlinear operators (47J15) Bifurcations in context of PDEs (35B32) Numerical bifurcation problems (65P30) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

Related Items (8)

Computer assisted proof to symmetry-breaking bifurcation phenomena in nonlinear vibration ⋮ Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem ⋮ Improved convergence theorems of Newton's method designed for the numerical verification for solutions of differential equations ⋮ Computer assisted proofs of bifurcating solutions for nonlinear heat convection problems ⋮ The Hopf bifurcation theorem in Hilbert spaces for abstract semilinear equations ⋮ Error analysis of Galerkin's method for semilinear equations ⋮ Codimension-\(m\) bifurcation theorems applicable to the numerical verification methods ⋮ Computer-assisted proofs of the existence of a symmetry-breaking bifurcation point for the Kolmogorov problem

Cites Work

• A bifurcation phenomenon for the periodic solutions of a semilinear dissipative wave equation
• A numerically based existence theorem for the Navier-Stokes equations
• Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points
• Computer assisted proof to symmetry-breaking bifurcation phenomena in nonlinear vibration
• Numerical verification of existence and inclusion of solutions for nonlinear operator equations
• Galerkin's procedure for nonlinear periodic systems
• Bifurcation from simple eigenvalues
• A geometric method of numerical solution of nonlinear equations and error estimation by Urabe's proposition
• The Computation of Symmetry-Breaking Bifurcation Points
• Periodic Solutions of Nonlinear Hyperbolie Partial Differential Equations
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