Sensitivity to initial condition on interval maps

Deterministic chaos is commonly characterized by sensitivity to initial conditions. This paper investigates the relationships between sensitivity, recurrence, and R-mixing in interval maps. We provide a characterization of R-mixing based on endpoint accessibility, establish links between sensitivity and recurrent interval cycles, and show that sensitive systems exhibit a unique recurrent structure. Our main results include new equivalence conditions for local eventual surjectivity, as well as explicit constructions of sensitive maps admitting a unique recurrent cycle.