Recurrence determinism, one of the fundamental characteristics of recurrencequantification analysis, measures predictability of a trajectory of a dynamicalsystem. It is tightly connected with the conditional probability that, given arecurrence, following states of the trajectory will be recurrences. In this paper we study recurrence determinism of interval dynamical systems.We show that recurrence determinism distinguishes three main types of$\omega$-limit sets of zero entropy maps: finite, solenoidal withoutnon-separable points, and solenoidal with non-separable points. As a corollarywe obtain characterizations of strongly non-chaotic and Li-Yorke (non-)chaoticinterval maps via recurrence determinism. For strongly non-chaotic maps,recurrence determinism is always equal to one. Li-Yorke non-chaotic intervalmaps are those for which recurrence determinism is always positive. Finally,Li-Yorke chaos implies the existence of a Cantor set of points with zerodeterminism.
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