publication . Preprint . 2017

Recurrence determinism and Li-Yorke chaos for interval maps

Špitalský, Vladimír;
Open Access English
  • Published: 08 Dec 2017
Abstract
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 $\omega$-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-)...
Subjects
Medical Subject Headings: animal structures
free text keywords: Mathematics - Dynamical Systems, 37E05 (Primary) 37B05, 54H20 (Secondary)
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