**Dynamical Systems (pure)**

[with M. Golubitsky] Hopf bifurcation in the presence of symmetry, Bull. Amer. Math. Soc. 11 (1984) 339-343.

[with M. Golubitsky] Hopf bifurcation in the presence of symmetry, Arch. Rational Mech. Anal. 87 (1985) 107-165.

[with M.Golubitsky] Hopf bifurcation with dihedral group symmetry: coupled nonlinear oscillators, in Multiparameter Bifurcation Theory (eds. M.Golubitsky and J.Guckenheimer), Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference, July 1985, Arcata; Contemporary Math. 56, Amer. Math. Soc., Providence RI 1986, 131-173.

[with J.Montaldi and R.M.Roberts] Nonlinear normal modes of symmetric Hamiltonian systems, in Structure Formation in Physics (eds. G.Dangelmayr and W.Güttinger), Springer-Verlag 1987, 354-371.

Stability of periodic solutions in symmetric Hopf bifurcation, Dynam. Stab. Sys. 2 (1987) 149-166.

[with M.Golubitsky] Generic bifurcation of Hamiltonian systems with symmetry, Physica D 24 (1987) 391-405. (With an appendix by J.E.Marsden.)

Bifurcations with symmetry, in New Directions in Dynamical Systems (eds. T.Bedford and J.W.Swift), London Math. Soc. Lecture Notes 127, Cambridge Univ. Press 1988, 235-283.

[with J.Montaldi and R.M.Roberts] Periodic solutions near equilibria of symmetric Hamiltonian systems, Phil. Trans. R. Soc. Lond. A 325 (1988) 237-293.

Order within the Chaos Game? The Dynamics Newsletter 3 #2-3 (1989) 4-9.

[with J.Montaldi and R.M.Roberts] Existence of nonlinear normal modes of symmetric Hamiltonian systems, Nonlinearity 3 (1990) 695-730.

[with J.Montaldi and R.M.Roberts] Stability of nonlinear normal modes of symmetric Hamiltonian systems, Nonlinearity 3 (1990) 731-772.

[with A.S. Hill] Hopf/steady-state mode interactions with O(2) symmetry, Dyn. Stab. Sys. 6 (1991) 149-171.

[with J.D.Crawford, M.Golubitsky, M.G.M.Gomes, and E.Knobloch] Boundary conditions as symmetry constraints, in Singularity Theory and its Applications — Warwick 1989, Part II: Singularities, Bifurcations, and Dynamics (eds. M.Roberts and I.Stewart), Lecture Notes in Mathematics 1463, Springer-Verlag, Heidelberg 1991, 63-79.

[with G.P.King] Symmetric chaos, in Nonlinear Equations in the Applied Sciences (eds. W.F.Ames and C.F.Rogers), Academic Press, New York 1991, 257-315.

[with M.J.Field and M.Golubitsky] Bifurcation on hemispheres, J. Nonlinear Sci. 1 (1991) 201-223.

Bifurcation theory old and new, in Dynamics of Numerics and Numerics of Dynamics (eds. D.S.Broomhead and A.Iserles, IMA Conference Series 34, Oxford University Press, Oxford 1992, 31-67.

[with H.Haaf and R.M.Roberts] A Hopf bifurcation with spherical symmetry, Z. Angew. Math. Phys. 43 (1992) 793-826.

[with M Golubitsky] An algebraic criterion for symmetric Hopf bifurcation, Proc. Roy. Soc. Lond. A 440 (1993) 727-732.

[with M.G.M.Gomes] Steady PDEs on generalized rectangles: a change of genericity in mode interactions, Nonlinearity 7 (1994) 253-272.

[with P.Ashwin and P.Chossat] Transitivity of orbits of maps symmetric under compact Lie groups, Chaos, Solitons and Fractals 4 (1994) 621-634.

[with P.Ashwin, G.Dangelmayr, and M.Wegelin] Oscillator networks with the symmetry of the unit quaternion group; in Dynamics, Bifurcation, and Symmetry (ed. P.Chossat), Proceedings, Cargèse 1993, NATO ASI Series C 437, Kluwer, Dordrecht 1994, 35-48.

[with J Buescu] Sets, lines, and adding machines, in Dynamics, Bifurcation, and Symmetry (ed. P.Chossat), Proceedings, Cargèse 1993, NATO ASI Series C 437, Kluwer, Dordrecht 1994, 59-68.

[with B.Dionne and M.Golubitsky] Coupled cells: wreath products and direct products, in Dynamics, Bifurcation, and Symmetry (ed. P.Chossat), Proceedings, Cargèse 1993, NATO ASI Series C 437, Kluwer, Dordrecht 1994, 1279-138.

[with M.G.M.Gomes] Hopf bifurcation on generalized rectangles with Neumann boundary conditions, in Dynamics, Bifurcation, and Symmetry (ed. P.Chossat), Proceedings, Cargèse 1993, NATO ASI Series C 437, Kluwer, Dordrecht 1994, 139-158.

[with P. Ashwin and J.Buescu] Bubbling of attractors and synchronization of chaotic oscillators, Phys. Lett. A 193 (1994) 126-139.

[with J.Buescu] Liapunov stability and adding machines, Ergod. Th. & Dynam. Sys. 15 (1995) 271-290.

[with M.Kroon] Detecting the symmetry of attractors for six oscillators coupled in a ring, Internat. J. Bif. Chaos 5 (1995) 209-229; prepublication in Hyperspace 4 (1995) 36-65.

[with B.Dionne, M.Golubitsky and M.Silber] Time-periodic spatially-periodic planforms in Euclidean equivariant PDE, Phil. Trans. Roy. Soc. London A 352 (1995) 125-168.

[with M.Golubitsky, J.E.Marsden, and M.Dellnitz] The Constrained Liapunov-Schmidt procedure and periodic orbits, Fields Institute Communications 4 (1995) 81-127; in Normal Forms and Homoclinic Chaos (eds. W.F.Langford and W.Nagata), Amer. Math. Soc., Providence RI 1995.

[with B.Dionne and M.Golubitsky] Coupled cells with internal symmetry: I. Wreath products, Nonlinearity 9 (1996) 559-574.

[with B.Dionne and M.Golubitsky] Coupled cells with internal symmetry: II. Direct products, Nonlinearity 9 (1996) 575-599.

[with P. Ashwin and J.Buescu] From attractor to chaotic saddle: a tale of transverse instability, Nonlinearity 9 (1996) 703-737.

[with M.G.M.Gomes] Symmetry of generic bifurcations in cubic domains, Internat. J. Bif. Chaos 7 (1997) 147-171.

[with I. Melbourne] Symmetric omega-limit sets for smooth Gamma-equivariant dynamical systems with Gamma-0 abelian, Nonlinearity 10 (1997) 1551-1567.

[with A.P.S. Dias] Hopf bifurcation on a simple cubic lattice, Dyn. Stab. Sys 14 (1999) 3-55.

[with M.Golubitsky] Symmetry and pattern formation in coupled cell networks, in Pattern Formation in Continuous and Coupled Systems (eds. M.Golubitsky, D.Luss, S.H.Strogatz), IMA volumes in Math. and Appns. 115, Springer, New York 1999, 65-82.

[with A.P.S. Dias] Symmetry-breaking bifurcations of wreath product systems, J. Nonlin. Sci. 9 (1999) 671-695.

[with A.P.S. Dias] Invariant theory for wreath product groups, J. Pure Appl. Algebra 150 (2000) 61-84.

[with A.P.S. Dias] Hilbert series for equivariant mappings restricted to invariant hyperplanes, J. Pure Appl. Algebra 151 (2000) 89-106.

[with A.P.S.Dias] Toric geometry and equivariant bifurcations, Physica D 143 (2000) 235-261. [Special issue dedicated to the memory of John David Crawford: Bifurcations, Patterns, and Symmetry.]

[with B.Dionne and A.P.S. Dias] Heteroclinic cycles and wreath product systems, Dyn. Stab. Sys. 15 (2000) 353-385.

[with M.Golubitsky] Patterns of oscillation in coupled cell systems, in

*Geometry, Dynamics and Mechanics: 60th Birthday Volume for J.E. Marsden*(eds. P.Holmes, P.Newton, and A.Weinstein), Springer-Verlag, New York 2002, 243-286.

Systems with emergent dynamics, in

*Computing Anticipatory Systems: CASYS 2001 - Fifth International Conference, Liége 2001*(ed. D.M.Dubois), AIP Conference Proceedings 627, Amer. Inst. Phys., New York 2002, 27-36.

Ruptura de la simetria, formació de patrons i caos simètric en sistemes dinàmics no lineals (Symmetry-breaking, pattern formation, and symmetric chaos in nonlinear dynamical systems), Butlletí Soc. Catalana Mat. 17 (2002) 123-141.

[with A.P.S. Dias] Secondary bifurcations in systems with all-to-all coupling, Proc. Roy. Soc. Lond. A 459 (2003) 1969-1986.

[with J.Buescu and M.Kulczycki] Liapunov stability and adding machines revisited, Dynamical Systems 21 (2006) 379-384.

[with M.Parker and M.G.M.Gomes] Forced symmetry-breaking of square lattice planforms, J. Dynam. Differential Equations 18 (2006) 223-255 [DOI: 10.1007/s10884-005-9004-z].

[with M. Parker] Examples of forced symmetry-breaking to homoclinic cycles in three-dimensional Euclidean-invariant systems, Internat. J. Bif. Chaos 18 (2008) 83-107.

[with M.Parker and M.G.M.Gomes] Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms, Dynamical Systems 23 (2008) 137-162.

[with M. Doebeli and T. Elmhirst] Pod systems: an equivariant ordinary differential equation approach to dynamical systems on a spatial domain, Nonlinearity 21 (2008) 1507-1531.

[with M. Parker and M.G.M. Gomes] Examples of forced symmetry-breaking to heteroclinic cycles and networks in three-dimensional Euclidean-invariant systems, Internat J. Bif. Chaos 19 (2009) 1655-1678.

Phase oscillators with sinusoidal coupling interpreted in terms of projective geometry, Internat. J. Bif. Chaos 21 (2011) 1795-1804.

Sources of uncertainty in deterministic dynamics: an informal overview, Phil. Trans. R. Soc. A 369 (2011) 4705-4729. [Theme issue, Handling Uncertainty in Science].

[with M. Golubitsky] Recent advances in symmetric and network dynamics,

*Chaos*25, 097612 (2015); DOI: 10.1063/1.4918595.