D. Armbruster, J. Guckenheimer, and P. Holmes (1988). Heteroclinic cycles and modulated travelling waves in systems with *O*(2) symmetry. *Phys. D*, **29**, 257–282.

V. Arnold (1978). *Mathematical Methods in Classical Mechanics*. Springer-Verlag, New York.

N. Aubry, P. Holmes, J.L. Lumley, and E. Stone (1988). The dynamics of coherent structures in the wall region of a turbulent boundary layer. *J. Fluid Mech.*, **192**, 115–173.

N. Aubry, J.L. Lumley, and P. Holmes (1989). The effect of drag reduction on the wall region. *Theoret. Comput. Fluid Dynamics*, submitted.

S. Barnett (1975). *Introduction to Mathematical Control Theory*. Clarendon Press, Oxford.

R.W. Brockett (1970). *Finite-Dimensional Linear Systems*. Wiley, New York.

R.W. Brockett (1972). Systems theory on group manifolds and coset spaces. *SIAM J. Control Optim.*, **10**, 265–284.

R. Hermann and A.J. Krener (1977). Nonlinear controllability and observability. *IEEE Trans. Automat. Control*, **22**, 725–740.

C. Jones and M. Proctor (1987). Strong spatial resonance and travelling waves in Bernard convection. *Phys. Lett. A*, **121**, 224–227.

V. Jurdjevic and J. Quinn (1978). Controllability and stability. *J. Differential Equations*, **28**, 381–389.

I. Kubo and J.L. Lumley (1980). A study to assess the potential for using long chain polymers dissolved in water to study turbulence. An. Rep. NASA-AMES Grant No. NSG-2382, Cornell University.

H. Kwakernaak and R. Sivan (1972). *Linear Optimal Control Systems*. Wiley-Interscience, New York.

J.L. Lumley (1967). The structure of inhomogeneous turbulent flows. In *Atmospheric Turbulence and Radio Wave Propagation* (ed. A.M. Yaglom and V.I. Tatarskii), pp. 166–178. Nauka, Moscow.

J.L. Lumley (1970). *Stochastic Tools in Turbulence*. Academic Press, New York.

J.L. Lumley (1981). Coherent structures in turbulence. In *Transition and Turbulence* (ed. R.E. Meyer), pp. 215–242. Academic Press, New York.

J.L. Lumley and I. Kubo (1984). Turbulent drag reduction by polymer additives; a survey. In *The Influence of Polymer Additives on Velocity and Temperature Fields. IUTAM Symposium, Essen*, 1984 (ed. B. Gampert), pp. 3–21, Springer-Verlag, Berlin.

J.L. Lumley, J.M. Guckenheimer, J.E. Marsden, P.J. Holmes, and S. Leibovich (1988). Structure and control of the wall region in a turbulent boundary layer. Proposal No. 88-NA-321, August, 1988.

B. Nicolaenko (1986). Lecture delivered at workshop on Computational Aspects of Dynamical Systems, Mathematical Sciences Institute, Cornell University, September 8–10, 1986.

L.P. Silnikov (1967). The existence of a denumerable set of periodic motions in four-dimensional space in an extended neighborhood of a saddle-focus. *Soviet Math. Dokl.*, **8**, 54–58.

J.J. Stoker (1950). *Nonlinear Vibrations*. Wiley, New York.

E. Stone and P. Holmes (1988). Random perturbations of heteroclinic attractors. Preprint.

H.J. Sussman and V. Jurdjevic (1972). Controllability of nonlinear systems. *J. Differential Equations*, **12**, 95–116.

A.J. van der Schaft (1986). Stabilization of Hamiltonian systems. *Nonlinear Anal. Theory Methods Applic.*, **10**, 1021–1035.

S. Wiggins (1988). *Global Bifurcations and Chaos*. Springer-Verlag, New York.