This volume contains the proceedings of two related workshops held at The Fields Institute in February and March 1993. The workshops were an integral part of the thematic year in Dynamical Systems and Bifurcation Theory held during the 1992-1993 academic year. This volume covers the full spectrum of research involved in combining symmetry methods with dynamical systems and bifurcation theory, from the development of the mathematical theory in order to understand the underlying mechanisms to the application of this new mathematical theory, to partial differential equation models of realistic physical phenomena. The individual contributions show the richness of the interplay between abstract methods and significant, essential examples.

D. Armbruster, E. Stone, and R. Heiland -- Towards analyzing the dynamics of flames 
A. Bayliss, B. J. Matkowsky, and H. Riecke -- Symmetries in modulated traveling waves in combustion: Jumping ponies on a merry-go-round 
H. S. Brown and L. G. Kevekidis -- Modulated traveling waves for the Kuramoto-Sivashinsky equation 
G. Caginalp -- Length scales in phase transition models: Phase field, Cahn-Hilliard, and blow-up problems 
D. J. Chillingworth -- Veronese and the detectives: Finding the symmetry of attractors 
J. D. Crawford -- $D_4$-symmetric maps with hidden Euclidean symmetry 
G. C. Cruywagen -- Modelling travelling waves of spatial patterning in morphogenesis 
G. d. Vries, R. M. Miura, and M. Pernarowski -- Analysis of models of pancreatic $beta$-cells exhibiting temporal pattern formation 
J. Duan -- Translating patterns in a generalized Ginzburg-Landau amplitude equation 
M. Field -- Geometric methods in bifurcation theory 
K. Gatermann and B. Werner -- Secondary Hopf bifurcation caused by steady-state steady-state mode interaction 
C. Geiger, G. Dangelmayr, J. D. Rodriguez, and W. Guttinger -- Symmetry breaking bifurcations in spherical Bernard convection. Part I: Results from singularity theory 
J. D. Rodriguez, C. Geiger, G. Dangelmayr, and W. Guttinger -- Symmetry breaking bifurcations in spherical Bernard convection. Part II: Numerical results 
W. D. Kalies and P. J. Holmes -- On a dynamical model for phase transformation in nonlinear elasticity 
E. Knobloch -- System symmetry breaking and Shil'nikov dynamics 
I. Milbourne -- Generalizations of a result on symmetry groups of attractors 
M. Menzinger and A. B. Rovinsky -- Instabilities induced by differential flows 
P. Ortoleva -- Self-organized zoning in crystals: Free boundaries, matched asymptotics, and bifurcation 
J. Scheurle -- Some aspects of successive bifurcations in the Couette-Taylor problem 
J. Wu -- Bifurcating waves in coupled cells described by delay-differential equations

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