Dynamics and Symmetry Group

Reprint List

University of Houston, Houston, TX 77204-3476

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COUPLED CELL SYSTEMS

[95] D. Gillis and M. Golubitsky, Patterns in square arrays of coupled cells. CHAOS. Submitted.

[95]  B. Dionne, M. Golubitsky and I. Stewart, Coupled cells with internal symmetry Part I: wreath products. Nonlinearity. Submitted.

[95] B. Dionne, M. Golubitsky and I. Stewart, Coupled cells with internal symmetry Part II: direct products. Nonlinearity. Submitted.

[95] M. Dellnitz, M. Field, M. Golubitsky, A. Hohmann and J. Ma. Cycling Chaos. Intern. J. Bifur. \& Chaos. To appear.

[94] M. Golubitsky, I. Stewart and B. Dionne, Coupled cells: wreath products and direct products. In: Dynamics, Bifurcation and Symmetry (P. Chossat, ed.) NATO ARW Series, Kluwer, Amsterdam, 1994, 127--138.

[93] I.R. Epstein and M. Golubitsky, Symmetric patterns in linear arrays of coupled cells. Chaos 3(1) (1993) 1-5.

[86] M. Golubitsky and I.N. Stewart, Hopf bifurcation with dihedral group symmetry: coupled nonlinear oscillators. In: Multiparameter Bifurcation Theory (M. Golubitsky and J. Guckenheimer, eds) Contemporary Mathematics 56, AMS (1986) 131-173.

SYMMETRIC CHAOS

[95] M. Field and M. Golubitsky, Symmetric chaos: how and why. Notices AMS 42 No. 2 (1995) 240-244.

[95] M. Golubitsky and M. Nicol, Symmetry Detectives for SBR attractors. Nonlinearity. To appear.

[94] M. Dellnitz, M. Golubitsky and M. Nicol, Symmetry of attractors and the Karhunen-Lo\'eve Decomposition. In: Trends and Perspectives in Applied Mathematics (L. Sirovich, ed.) Appl. Math. Sci. 100, Springer-Verlag, New York, 1994, 73-108.

[94] M. Field, M. Golubitsky and M. Nicol, A note on symmetries of invariant sets with compact group actions. In: Equadiff 8. Tatra Mountains Math. Publ. 4 (1994) 93-104.

[93] E. Barany, M. Dellnitz and M. Golubitsky, Detecting the symmetry of attractors. Physica D 67 (1993) 66-87.

[93] I. Melbourne, M. Dellnitz and M. Golubitsky, The structure of symmetric attractors. Arch. Rational Mech. Anal. 123 (1993) 75-98.

[93] M. Field and M. Golubitsky, Symmetries on the edge of chaos. New Scientist, 1855, January 9, 1993, 32-35.

[92] M. Dellnitz, M. Golubitsky and I. Melbourne, Mechanisms of symmetry creation. In: Bifurcation and Symmetry (E. Allgower, K. B\"ohmer and M. Golubitsky, eds.), ISNM 104, Birkh\"ausser, Basel, 1992, 99-109.

[92] M. Field and M. Golubitsky, Symmetry in Chaos: A Search for Pattern in Mathematics, Art, and Nature. Oxford University Press, Oxford, 1992.

German translation by Micha Lotrovsky: Chaotische Symmetrien, Birkhauser Verlag, Basel, 1993.

French translation by Christian Jeanmougin: La Symetrie du Chaos, InterEditions, Paris, 1993.

[90] M. Field and M. Golubitsky, Symmetric chaos. Computers in Physics. Sep/Oct 1990, 470-479.

[88] P. Chossat and M. Golubitsky, Symmetry increasing bifurcation of chaotic attractors. Physica D 32 (1988) 423-436.

BIFURCATION AND SYMMETRY

[95] B. Dionne, M. Golubitsky, M. Silber and I. Stewart, Time-periodic spatially-periodic planforms in Euclidean equivariant systems. Phil. Trans. R. Soc. London A 352 (1995) 125-168.

[95]  M. Field, Symmetry breaking for compact Lie groups, Mem. Amer. Math. Soc to appear.

[93] M. Golubitsky and I.Stewart, An algebraic criterion for symmetric Hopf bifurcation. Proc. R. Soc. London. 440 (1993) 727-732.

[92] B. Dionne and M. Golubitsky, Planforms in two and three dimensions. ZAMP. 43 (1992) 36-62.

[92] I. Stewart and M. Golubitsky, Fearful Symmetry: Is God a Geometer?. Blackwell Publishers, Oxford, 1992.

German translation by Hanjo Schnug: Denkt Gott symmetrisch? Das Ebenmass in Mathematik und Natur, Birkhauser Verlag, Basel, 1993.

Dutch translation by Hans van Cuijlenborg: Turings tijger, Epsilon Uitgaven, Utrecht, 1994.

Italian translation by Libero Sosio: Terribili simmetrie Dio e un geometra? , Saggi Scientifici, Bollati Borighieri, Torino 1995.

[92] E. Allgower, K. Bohmer and M. Golubitsky. Bifurcation and Symmetry, ISNM 104, Birkhauser, Basal, 1992.

[91] M. Field, M. Golubitsky and I.N. Stewart, Bifurcations on hemispheres. J. Nonlinear Science 1 (1991) 201-223.

[91] J.D. Crawford, M.Golubitsky, M.G.M. Gomes, E. Knobloch and I.N. Stewart, Boundary conditions as symmetry constraints. Singularity Theory and Its Applications, Warwick 1989, Part II. (M. Roberts and I.N. Stewart, eds), Lecture Notes in Math. 1463, Springer-Verlag, Heidelberg, 1991, 63-79.

[91] M. Golubitsky, Genericity, bifurcation and symmetry. In: Patterns and Dynamics in Reactive Media (H.L. Swinney, R. Aris and D.G. Aronson, eds.). IMA Volumes in Mathematics and its Applications, Volume 37. Springer-Verlag, New York, 1991, 71-88.

[90] S.A. van Gils and M. Golubitsky, A torus bifurcation theorem in the presence of symmetry. Dyn. Diff. Eqn. 2, No. 2 (1990) 133-163.

[89] Li Kaitai, J. Marsden, M. Golubitsky and G. Iooss, Bifurcation Theory and Its Numerical Analysis, Xi'an Jiaotong University Press, Xi'an China, 1989.

[89] A. Vanderbauwhede, M. Krupa and M. Golubitsky, Secondary bifurcations in symmetric systems. Differential Equations, Lect. Notes Pure Appl. Math. 118 (C.M. Dafermos, G. Ladas and G. Papanicolaou, Eds.) Marcel Dekker, Inc., New York, 1989, 709-716.

[88] M. Golubitsky, I.N. Stewart and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory: Vol. II. Applied Mathematical Sciences 69. Springer-Verlag, New York, 1988.

[88] P. Chossat and M. Golubitsky, Iterates of maps with symmetry. SIAM J. Math. Anal. 19, No. 6 (1988) 1259-1270.

[88] J.D. Crawford, M. Golubitsky and W.F. Langford, Modulated rotating waves in O(2) mode interactions. Dyn. Stab. Sys. 3, No. 3-4 (1988) 159-175.

[87] M. Golubitsky and I.N. Stewart, Generic bifurcation of Hamiltonian systems with symmetry. Physica D 24 (1987) 391-405.

[87] M. Golubitsky and M. Roberts, Degenerate Hopf bifurcation with O(2) symmetry. J. Diff. Eqn. 69 (1987) 216-264.

[87] P. Chossat and M. Golubitsky, Hopf bifurcation in the presence of symmetry, center manifold and Liapunov-Schmidt reduction. In: Oscillation, Bifurcation and Chaos (F.V. Atkinson, W.F. Langford and A.B. Mingarelli, eds.) CMS-AMS Conf. Proc. Ser.8 (1987), AMS, Providence, 343-352.

[86] P. Chossat, M. Golubitsky and B.L. Keyfitz, Hopf-Hopf mode interactions with O(2) symmetry. Dyn. Stab. Sys. 1, No. 4 (1986) 255-292.

[86] M. Golubitsky and J. Guckenheimer, Multiparameter Bifurcation Theory, Contemporary Mathematics 56, AMS, 1986.

[86] M. Golubitsky and I.N. Stewart, Symmetry and Stability in Taylor-Couette flow. SIAM J. Math. Anal. 17 No. 2 (1986) 249-288.

[85] M. Golubitsky and I.N. Stewart, Hopf bifurcation in the presence of symmetry. Arch. Rational Mech. Anal. 87 No. 2 (1985) 107-165.

See also: Bull. AMS 11 No. 2 (1984) 339-342.

[84] E. Ihrig and M. Golubitsky, Pattern selection with O(3) symmetry. Physica 13D (1984) 1-33.

[84] M. Golubitsky, J. Marsden and D. Schaeffer, Bifurcation problems with hidden symmetries. Partial Differential Equations and Dynamical Systems (W.E. Fitzgibbon III, ed.) Res. Notes in Math. 101 Pitman Press. (1984) 181-210.

[83] M. Golubitsky, The Benard problem, symmetry and the lattice of isotropy subgroups. Bifurcation Theory, Mechanics and Physics (C.P. Bruter et al. eds.) D. Reidel Publishing Co. (1983) 225-256.

[83] M. Golubitsky and D. Schaeffer, A discussion of symmetry and symmetry breaking. Singularity Theory {P. Orlik, ed. Proc. Symp. Pure Math. 40 (1983) 499-516.

[81] D. Schaeffer and M. Golubitsky, Bifurcation analysis near a double eigenvalue of a model chemical reaction. Arch. Rational Mech. & Anal. 75 (1981) 315-347.

APPLICATIONS

[92] W.W. Farr and M. Golubitsky, Rotating chemical waves in the Gray-Scott model. SIAM J. Appl. Math. . 52 No.1 (1992) 181-221.

[91] M. Golubitsky, M. Krupa and C. Lim, Time-reversibility and particle sedimentation. SIAM J. Appl. Math. 51 No. 1 (1991) 49-72.

[91] D.G. Aronson, M. Golubitsky and M. Krupa, Large arrays of Josephson junctions and iterates of maps with S_n symmetry. Nonlinearity. 4 (1991) 861-902.

[91] D.G. Aronson, M. Golubitsky and J. Mallet-Paret, Ponies on a merry-go-round in large arrays of Josephson junctions. Nonlinearity. 4 (1991) 903-910.

[88] M. Golubitsky and W.F. Langford, Pattern formation and bistability in flow between counterrotating cylinders. Physica D 32 (1988) 362-392

[88] W.F. Langford, R. Tagg, E. Kostelich, H.L. Swinney and M. Golubitsky, Primary instability and bicriticality in flow between counterrotating cylinders. Phys. Fluids. 31(4) (1988) 776-785.

[86] B.L. Keyfitz, M. Golubitsky, M. Gorman and P. Chossat, The use of symmetry and bifurcation techniques in studying flame stability. In: Reacting Flows: Combustion and Chemical Reactors (G.S.S. Ludford, ed.). Lectures in Appl. Math. 24, Part 2, AMS, Providence, 1986, 293-315.

[84] M. Golubitsky, J.W. Swift and E. Knobloch, Symmetries and Pattern selection in Rayleigh-Benard convection. Physica 10D (1984) 249-276.

[83] E. Buzano and M. Golubitsky, Bifurcation involving the hexagonal lattice and the planar Benard problem. Phil. Trans. Roy. Soc. London A308 (1983) 617-667.

See also: E. Buzano and M. Golubitsky, Bifurcation involving the hexagonal lattice. Proc. Symp. Pure Math. 40 (1983) 203-210.

[82] M. Golubitsky and D. Schaeffer, Bifurcation with O(3) symmetry including applications to the Benard problem. Commun. Pure \& Appl. Math. 35 (1982) 81-111.

[81] M. Golubitsky, B.L. Keyfitz and D. Schaeffer, A singularity theory analysis of the thermal chainbranching model. Commun. Pure & Appl. Math. 34 (1981) 433-463.

[80] M. Golubitsky and B.L. Keyfitz, A qualitative study of the steady-state solutions for a continuous flow stirred tank chemical reactor. SIAM J. Math. Anal. 11 (1980) 316-339.

[79] D. Schaeffer and M. Golubitsky, Boundary conditions and mode jumping in the buckling of a rectangular plate. Commun. Math. Phys. 69 (1979) 209-236.

[75] M. Golubitsky and D. Schaeffer, Stability of shock waves for a single conservation law. Adv. Math. 16 No. 1 (1975) 65-71.

[75] M. Golubitsky, E. Keeler and M. Rothschild, Convergence of the age structure: applications of the projective metric. Theor. Pop. Biol. 7 No. 1 (1975) 84-93.

SINGULARITY THEORY

[95] M. Golubitsky, J. Marsden, I. Stewart and M. Dellnitz, The constrained Liapunov-Schmidt procedure and periodic orbits. Fields Institute Proceedings. To appear.

[85] M. Golubitsky and D.G. Schaeffer, Singularities and Groups in Bifurcation Theory: Vol. I. Applied Mathematical Sciences 51. Springer-Verlag, New York, 1985.

[83] M. Golubitsky and J. Marsden, The Morse lemma in infinite dimensions via singularity theory. SIAM J. Math. Anal. 14 (1983) 1037-1044.

[81] M. Golubitsky and W.F. Langford, Classification and unfoldings of degenerate Hopf bifurcation. J. Diff. Eqns. 41 (1981) 375-415.

[79] M. Golubitsky and D. Schaeffer, A theory for imperfect bifurcation via singularity theory. Commun. Pure and Appl. Math. 32 (1979) 1-77.

[79] M. Golubitsky and D. Schaeffer, Imperfect bifurcation in the presence of symmetry. Commun. Math. Phys. 67 (1979) 205-232.

See also: M. Golubitsky and D. Schaeffer, A qualitative approach to steady state bifurcation theory. New Approaches to Nonlinear Problems in Dynamics, SIAM (1980) 43-52, 257-270, 433-436.

M. Golubitsky and D. Schaeffer, A singularity theory approach to steady state bifurcation theory. Nonlinear Partial Differential Equations and Applied Science, Dekker (1980) 229-254.

M. Golubitsky and D. Schaeffer, An analysis of imperfect bifurcation. Annals of New York Acad. of Sci. 316 (1979) 127-133.

[79] M. Golubitsky, A review of Catastrophe Theory and its Applications by Tim Poston and Ian Stewart. Bull. AMS 1 No. 3 (1979) 524-532.

[78] M. Golubitsky, An introduction to catastrophe theory and its applications. SIAM Review 20 No. 2 (1978) 352-387.

[78] M. Golubitsky and D. Tischler, A survey on the singularities and stability of differential forms. Asterisque 59-60 (1978) 43-82.

[77] M. Golubitsky and D. Tischler, An example of moduli for singular symplectic forms. Inventiones Math. 38 (1977) 219-225.

[76] M. Golubitsky and D. Tischler, On the non-existence of globally stable forms. Proc. AMS 58 (1976) 296-300.

[76] M. Golubitsky and D. Tischler, On the local stability of differential forms. Trans. AMS 223 (1976) 205-221.

[75] M. Golubitsky and V. Guillemin, Contact equivalence for Lagrangian submanifolds. Adv. Math. 15 No. 3 (1975) 375-387.

See also: M. Golubitsky, Contact equivalence for Lagrangian submanifolds. Dynamical Systems-Warwick 1974. Lecture Notes Math. 468. Springer Verlag. New York, 1975, 71-73.

[73] M. Golubitsky and V. Guillemin, Stable Mappings and Their Singularities. Graduate Texts in Math. 14, Springer-Verlag, New York, 1973. Second printing 1980, third printing 1986.

Russian translation by A. Kushnirenko: Mir, Moscow, 1976.

HETEROCLINIC CYCLES

[95] C. Hou and M. Golubitsky, An example of symmetry breaking to heteroclinic cycles, J. Diff. Eqn. Submitted.

[89] I. Melbourne, P. Chossat and M. Golubitsky, Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry. Proc. Roy. Soc. Edinburgh 113A (1989) 315-345.

OTHER

[95] M. Golubitsky, J.-M. Mao and M. Nicol, Symmetries of periodic solutions for planar potential systems. Proc. Amer. Math. Soc. To appear.

[95] M. Dellnitz, M. Golubitsky, A. Hohmann and I. Stewart, Spirals in scalar reaction diffusion equations. Intern. J. Bifur. \& Chaos. To appear.

[92] E. Barany, M. Golubitsky and J. Turski. Bifurcations with local gauge symmetries in the Ginzburg-Landau equations. Physica D56 (1992) 36-56.

[81] M. Golubitsky and H.L. Smith, A remark on periodically perturbed bifurcation. Differential Equations and Applications to Ecology, Epidemics and Population Problems. Academic Press (1981) 259-277.

[72] M. Golubitsky, Primitive actions and maximal subgroups of Lie groups. J. Diff. Geom. 7 (1972) 175-191.

[71] M. Golubitsky and B. Rothschild, Primitive subalgebras of exceptional Lie algebras. Pac. J. Math. 39 No. 2 (1971) 371-393.

See also: Bull. AMS 77 No. 6 (1971) 983-986.