M. Golubitsky

Publications
Influence

Singularities and groups in bifurcation theory

M. Golubitsky, D. Schaeffer
Mathematics, Physics
1985

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 this… Expand

2,807
243

Stable mappings and their singularities

M. Golubitsky, V. Guillemin
Mathematics
1973

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

1,606
120

Patterns of Synchrony in Coupled Cell Networks with Multiple Arrows

M. Golubitsky, I. Stewart, A. Török
Mathematics, Computer Science
SIAM J. Appl. Dyn. Syst.
22 February 2005

A coupled cell system is a network of dynamical systems, or "cells," coupled together. Expand

Symmetry Groupoids and Patterns of Synchrony in Coupled Cell Networks

I. Stewart, M. Golubitsky, M. Pivato
Mathematics, Computer Science
SIAM J. Appl. Dyn. Syst.
2003

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

The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space

M. Golubitsky, I. Stewart
Mathematics
22 March 2002

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

Singularities and Groups in Bifurcation Theory: Volume I

M. Golubitsky, I. Stewart
Physics
5 December 1984

Nonlinear dynamics of networks: the groupoid formalism

M. Golubitsky, I. Stewart
Mathematics
3 May 2006

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

The Symmetry Perspective

Pattern selection with O(3) symmetry

E. Ihrig, M. Golubitsky
Mathematics
1 August 1984

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 isotropy… Expand

Hopf Bifurcation in the presence of symmetry

M. Golubitsky, I. Stewart
Mathematics
1 October 1984

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 discuss… Expand

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