Dynamical intricacy and average sample complexity. Issue 3 (3rd July 2018)

• Record Type: Journal Article
• Authors: Petersen, Karl; Wilson, Benjamin
• Is Part Of: Dynamical systems. Volume 33:Issue 3(2018)
• Page Start: 369
• Page End: 418
• Publication Date: 2018-07-03
• Subjects: Entropy -- complexity -- intricacy -- ergodic theory -- topological dynamics; Primary 37B40 -- 37A35 -- 54H20 -- 28D20; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2017.1374352
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: We propose a new way to measure the balance between freedom and coherence in a dynamical system and a new measure of its internal variability. Based on the concept of entropy and ideas from neuroscience and information theory, we define intricacy and average sample complexity for topological and measure-preserving dynamical systems. We establish basic properties of these quantities, show that their suprema over covers or partitions equal the ordinary entropies, compute them for many shifts of finite type, and indicate natural directions for further research.