Equivariant multiparameter bifurcation via singularity theory

DOI10.1007/BF01053160zbMath0778.58014OpenAlexW2006886762MaRDI QIDQ2368046

Yung-Chen Lu, Ali Lari-Lavassani

Publication date: 22 August 1993

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

Full work available at URL: https://doi.org/10.1007/bf01053160

zbMATH Keywords

normal formsfinite determinacysingularity of mappingsstability of equivariant bifurcationstructural stability of universal unfoldings

Mathematics Subject Classification ID

Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25) Local and nonlocal bifurcation theory for dynamical systems (37G99) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

Related Items (10)

Equivariant multiparameter bifurcation via singularity theory ⋮ Singular analysis of bifurcation systems with two parameters ⋮ Bifurcation characteristics analysis of a class of nonlinear dynamical systems based on singularity theory ⋮ A tangent space characterisation of the equivalence of germs for geometric subgroups of and ⋮ Path formulation for multiparameter \(\mathbb D_3\)-equivariant bifurcation problems ⋮ Unfolding of multiparameter equivariant bifurcation problems with two groups of state variables under left-right equivalent group ⋮ Stability of equivariant bifurcation problems with two types of state variables and their unfoldings in presence of parameter symmetry ⋮ Multiple Buckling and Codimension-Three Bifurcation Phenomena of a Nonlinear Oscillator ⋮ Symmetry-breaking bifurcations on multidimensional fixed point subspaces ⋮ Bifurcation analysis of composite laminated piezoelectric rectangular plate structure in the case of 1:2 internal resonance

Cites Work

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• Singularities and groups in bifurcation theory. Volume I
• Stability of unfoldings in the context of equivariant contact- equivalence
• Stability of G-unfoldings
• Singularities and groups in bifurcation theory. Volume II
• Equivariant multiparameter bifurcation via singularity theory
• The unfolding and determinacy theorems for subgroups of 𝒜 and 𝒦
• Persistence of bifurcation diagrams in the presence of symmetry
• A singularity theory analysis of bifurcation problems with octahedral symmetry
• The recognition problem for equivariant singularities
• On the Stability of Equivariant Bifurcation Problems and Their Unfoldings
• Transversality in G-Manifolds
• A theory for imperfect bifurcation via singularity theory
• Generic bifurcations of varieties

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