Sensitivity to initial condition on interval maps

Abstract

One of the most characteristic attributes of deterministic chaos is sensitivity to initial condition.   This paper explores relationships between sensitivity to initial conditions, recurrence, and R-mixing in interval maps. We characterize R-mixing through endpoint accessibility, establish connections between sensitivity and recurrent interval cycles, and demonstrate uniqueness of recurrent structures in sensitive systems. Key results include equivalence conditions for local eventual surjectivity and constructions of sensitive maps with unique recurrent cycles.