Recent developments in the digital approach of symbolic dynamics
Κώστας Καραμάνος, Aristotelis S. Gkiolmas, Constantine D. Skordoulis · Kybernetes · 2011
Purpose The purpose of this paper is to explore new mathematical results to advance the understanding of the picture of a chaotic unimodal map. Design/methodology/approach Ever since Poicare, deterministic chaos is ultimately connected with exponential divergence of nearby trajectories, unpredictability and erratic behaviour. Here, the authors propose an alternative approach in terms of complexity theory and transcendence. Findings In this paper, the authors were able to reproduce previous results easily, due to new theorems. Originality/value The paper updates previous results and proposes a more complete understanding of the phenomenon of deterministic chaos, also making possible connections with number theory, combinatorics and possibly quantum mechanics, as in quantum mechanics there does not exist the notion on nearby trajectories.