ON THE ENTROPY OF A HALF SYNCHRONIZING SPACE

Abstract

To establish the concept of half synchronized entropy, we must first clarify the
conditions under which a subshift can be deemed half synchronized. This characterization involves
analyzing the block structure inherent in the subshift, focusing on how certain patterns can repeat over time, albeit with some restrictions. Unlike fully synchronized systems where a global periodic structure dominates, half synchronized systems allow for greater complexity while still maintaining a semblance of order. This duality between complexity and order forms the crux of half synchronized entropy. Nearly sofic systems have been known to exhibit rich and intricate behaviors, bridging the gap between symbolic dynamics and more conventional dynamical systems. The exploration of these connections paves the way for further advancements in the study of synchronized systems and their entropy properties.