Weakly attracting repellors for piecewise convex maps (Q1202766)

The author introduces the notion of a ``weakly attracting repellor'' which is an unstable fixed point such that the trajectories stay in its neighborhood for an extremely long time. He studies a class of piecewise convex increasing maps which includes some intermittent dynamical systems and a class of cusp type maps which is related to the Lorenz equation with a critical parameter. He also proves that if piecewise convex maps have weak attracting repellors under some condition the Lyapunov number is 0 for almost every point. The proofs use a specially defined \(\sigma\)- finite invariant measure.