A new randomness-generating mechanism in forced relaxation oscillations

This note points out that in a wide class of forced relaxation oscillators the hyperbolic behavior, which has up to now been known to exist only on small set, dominates in the Lebesgue sense in a wide class of relaxation oscillators. This note introduces the simplest physically realistic smooth system where the strange attractor is expected to exist for most (in the Lebesgue sense) parameter values. This phenomenon went unobserved for over half a century since the first work on forced relaxation oscillations by Cartwright, Littlewood and Levinson.