Journal ArticleDOI
Steady-State bifurcation with 0(3)-Symmetry
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This article is published in Archive for Rational Mechanics and Analysis.The article was published on 1991-12-01. It has received 109 citations till now. The article focuses on the topics: Steady state (electronics) & Symmetry (physics).read more
Citations
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Positive and sign changing solutions to a nonlinear Choquard equation
Mónica Clapp,Dora Salazar +1 more
TL;DR: In this paper, the authors considered the problem of finding a positive solution and multiple sign changing solutions to the problem with small energy, under symmetry assumptions on Ω and W, which allow finite symmetries, and some assumptions on the decay of W at infinity.
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Planforms in two and three dimensions
Benoit Dionne,Martin Golubitsky +1 more
TL;DR: In this article, the authors used group theoretic techniques to determine a large class of spatially doubly periodic solutions that are forced to existence near a steady-state bifurcation from a translation-invariant equilibrium.
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A short treatise on the equivariant degree theory and its applications
TL;DR: In this paper, the authors give a profound introduction to equivariant degree theory, avoiding as far as possible technical details and highly theoretical background, focusing on algebraic, analytical and topological tools for its effective calculation, the latter being illustrated by six concrete examples.
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Heteroclinic cycles in dynamical systems with broken spherical symmetry
Reiner Lauterbach,Mark Roberts +1 more
TL;DR: In this article, it was shown that spontaneous symmetry breaking may also give rise to more complex dynamical behavior, in particular to heteroclinic cycles, and a simple example of their constructions (for the particular choices of groups G = SO (3), H = SO(2), and K = T, described below) in order to illustrate these general ideas.
References
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Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
BookDOI
Singularities and groups in bifurcation theory
TL;DR: Singularities and groups in bifurcation theory as mentioned in this paper have been used to solve the problem of finding a group of singularities in a set of problems with multiple solutions.