Global Attractors and Chaos of Complex Bernoulli-shift Rules

Abstract

This paper provides a symbolic dynamics perspective to Chua’s topologically-distinct complex Bernoulli-shift rules 18, 122, 126 and 146. Through this work, a rigorous analysis of their global attractors is conducted in the space of bi-infinite symbolic sequences. Based on the concepts of blocking transformation and releasing transformation, their chaotic dynamics is further uncovered, including topological mixing and positive topological entropy.