  We report the observation of dynamical behaviour in dilute, aqueous solutions
of a surfactant CTAT (cetyl trimethylammonium p-toluenesulphonate), below the
overlap concentration c$^{\star}$. At these concentrations, CTAT forms
cylindrical micelles and shows a pronounced shear thickening transition above a
concentration-dependent critical shear rate $\dot\gamma_{c}$. An analysis of
the time-series of the stress relaxations at controlled shear rates in the
shear-thickening regime shows the existence of correlation dimensions greater
than two and positive Lyapunov exponents. This indicates the existence of
deterministic chaos in the dynamics of stress relaxation at these
concentrations and shear rates. The observed chaotic behaviour may be
attributed to the stick-slip between the shear - induced structure (SIS) formed
in the sheared surfactant solution and the coexisting dilute phase. At still
higher shear rates, when the SIS spans the Couette, there is a transition to
higher-dimensional dynamics arising out of the breakage and recombination of
the SIS.
