• Publications
  • Influence
Infinite-dimensional Lie algebras
1. Basic concepts.- 1. Preliminaries.- 2. Nilpotency and solubility.- 3. Subideals.- 4. Derivations.- 5. Classes and closure operations.- 6. Representations and modules.- 7. Chain conditions.- 8.Expand
  • 2,724
  • 357
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
  • 230
  • 39
  • PDF
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
  • 276
  • 30
  • PDF
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
  • 261
  • 29
  • PDF
TA Today: A New Introduction to Transactional Analysis
TLDR
Anti-microbial compositions comprising an inert carrier and a defined class of di-aryl nitrones with fungicidal activity against a broad spectrum of plant pathogenic fungi. Expand
  • 226
  • 29
  • PDF
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
  • 328
  • 24
  • PDF
The Symmetry Perspective
  • 261
  • 24
From attractor to chaotic saddle: a tale of transverse instability
Suppose that a dynamical system possesses an invariant submanifold, and the restriction of the system to this submanifold has a chaotic attractor A. Under which conditions is A an attractor for theExpand
  • 288
  • 18
  • PDF
Does God Play Dice? The New Mathematics of Chaos
Preface to the Second Edition. Prologue: Clockwork or Chaos? 1. Chaos from Order. 2. Equations for Everything. 3. The Laws of Error. 4. The Last Universalist. 5. One-way Pendulum. 6. StrangeExpand
  • 480
  • 16
The collapse of chaos : discovering simplicity in a complex world
Simplicity and complexity the laws of nature the organization of development the possibilities of evolution the origins of human understanding systems of interactive behaviour complexity andExpand
  • 460
  • 16
  • PDF