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A kinetic approach is adopted to describe the exponential growth of a smalldeviation of the initial phase space point, measured by the largest Lyapunovexponent, for a dilute system of hard disks, both in equilibrium and in auniform shear flow. We derive a generalized Boltzmann equation for an extendedone-particle distribution that includes deviations from the reference phasespace point. The equation is valid for very low densities n, and requires anunusual expansion in powers of 1/|ln n|. It reproduces and extends results fromthe earlier, more heuristic clock model and may be interpreted as describing afront propagating into an unstable state. The asymptotic speed of propagationof the front is proportional to the largest Lyapunov exponent of the system.Its value may be found by applying the standard front speed selection mechanismfor pulled fronts to the case at hand. For the equilibrium case, an explicitexpression for the largest Lyapunov exponent is given and for sheared systemswe give explicit expressions that may be evaluated numerically to obtain theshear rate dependence of the largest Lyapunov exponent.Comment: 26 pages REVTeX, 1 eps figure. Added remarks, a reference and  corrected some typo

Front propagation techniques to calculate the largest Lyapunov exponent of dilute hard disk gases