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Singularities and groups in bifurcation theory
This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob- lems and we hope to convert the reader to thisExpand
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Stable mappings and their singularities
I: Preliminaries on Manifolds.- 1. Manifolds.- 2. Differentiable Mappings and Submanifolds.- 3. Tangent Spaces.- 4. Partitions of Unity.- 5. Vector Bundles.- 6. Integration of Vector Fields.- II:Expand
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Patterns of Synchrony in Coupled Cell Networks with Multiple Arrows
TLDR
A coupled cell system is a network of dynamical systems, or "cells," coupled together. Expand
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Symmetry Groupoids and Patterns of Synchrony in Coupled Cell Networks
TLDR
A coupled cell system is a set of cells with coupling, that is, a dynamical system whose variables correspond to cells, such that the output of certain cells affects the time-evolution of other cells. Expand
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The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space
1. Steady-State Bifurcation.- 1.1. Two Examples.- 1.2. Symmetries of Differential Equations.- 1.3. Liapunov-Schmidt Reduction.- 1.4. The Equivariant Branching Lemma.- 1.5. Application to Speciation.-Expand
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Singularities and Groups in Bifurcation Theory: Volume I
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Nonlinear dynamics of networks: the groupoid formalism
A formal theory of symmetries of networks of coupled dynamical systems, stated in terms of the group of permutations of the nodes that preserve the network topology, has existed for some time.Expand
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The Symmetry Perspective
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Pattern selection with O(3) symmetry
Abstract For each irreducible representation of SO(3) and O(3) we determine, up to conjugacy, all isotropy subgroups and identify, in particular, the maximal isotropy subgroups. Each isotropyExpand
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Hopf Bifurcation in the presence of symmetry
Using group theoretic techniques, we obtain a generalization of the Hopf Bifurcation Theorem to differential equations with symmetry, analogous to a static bifurcation theorem of Cicogna. We discussExpand
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