Scaling of Lyapunov exponents at nonsmooth bifurcations

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Abstract
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 dimension. We show that the largest Lyapunov exponent λ has a discontinuous jump at the bifurcation and the scaling when the bifurcation parameter ε is λ∼1/‖lnε‖. For a similar class of discontinuous maps there can be no immediate transition to intermittent chaos.