H. Lamba et Cj. Budd, SCALING OF LYAPUNOV EXPONENTS AT NONSMOOTH BIFURCATIONS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 50(1), 1994, pp. 84-90
In nonsmooth maps intermittency can arise when a periodic orbit loses
stability by crossing a set where the mapping is nondifferentiable. Mo
tivated by the impact oscillator, which gives rise to a discontinuous
mapping with infinite stretching, we consider classes of continuous bu
t nondifferentiable maps in one and two dimensions. We show that the l
argest Lyapunov exponent lambda has a discontinuous jump at the bifurc
ation and the scaling when the bifurcation parameter epsilon is lambda
approximately 1/\In epsilon\. For a similar class of discontinuous ma
ps there can be no immediate transition to intermittent chaos.