SCALING OF LYAPUNOV EXPONENTS AT NONSMOOTH BIFURCATIONS

In nonsmooth maps intermittency can arise when a periodic orbit loses stability by crossing a set where the mapping is nondifferentiable. Motivated by the impact oscillator, which gives rise to a discontinuous mapping with infinite stretching, we consider classes of continuous but nondifferentiable maps in one and two dimensions. We show that the largest Lyapunov exponent lambda has a discontinuous jump at the bifurcation and the scaling when the bifurcation parameter epsilon is lambda approximately 1/\In epsilon\. For a similar class of discontinuous maps there can be no immediate transition to intermittent chaos.