2017/12/08 by Vladimı́r Špitalský, Špitalský, Vladimír
Engineering · Mathematics · Physics and Astronomy · #37E05 (Primary) 37B05 #54H20 (Secondary) #Artificial Immune Systems Applications #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1712.03023
openalex publication_date 2017/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Recurrence determinism, one of the fundamental characteristics of recurrence quantification analysis, measures predictability of a trajectory of a dynamical system. It is tightly connected with the conditional probability that, given a recurrence, 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 ω-limit sets of zero entropy maps: finite, solenoidal without non-separable points, and solenoidal with non-separable points. As a corollary we obtain characterizations of strongly non-chaotic and Li-Yorke (non-)chaotic interval maps via recurrence determinism. For strongly non-chaotic maps, recurrence determinism is always equal to one. Li-Yorke non-chaotic interval maps are those for which recurrence determinism is always positive. Finally, Li-Yorke chaos implies the existence of a Cantor set of points with zero determinism.