Unusual chaotic attractors in nonsmooth dynamic systems

The present paper describes an unusual example of chaotic motion occurring in a nonsmooth mechanical system affected by dry friction. The mechanical system generates one-dimensional maps the orbits of which seem to exhibit sensitive dependence on initial conditions only in an extremely small set of their field of definition. The chaotic attractor is composed of zones characterized by very different rates of divergence of nearby orbits: in a large portion of the chaotic attractor the system motion follows a regular pattern whereas the more usual irregular motion affects only a small portion of the attractor. The irregular phase reintroduces the orbit in the regular zone and the sequence is repeated. The Lyapunov exponent of the map is computed to characterize the steady state motions and confirm their chaotic nature