Special Issue "Entropic Properties of Dynamical Systems"
A special issue of Entropy (ISSN 1099-4300).
Deadline for manuscript submissions: closed (30 October 2016).
Interests: measure-theoretic entropy; topological entropy; amenable entropy; operator entropy; symbolic extensions; law of series; chaos
Dynamical systems, regardless of the wide range of objects that can be understood under this name, can be classified into three main classes: zero entropy, finite positive entropy, and infinite entropy systems. Zero entropy systems are those with slow (subexponential) complexity (whatever that means), finite positive entropy systems usually reveal some kind of randomness or chaos, and so do infinite entropy systems, but surprisingly they share some abilities of zero entropy systems, for example they can be self-similar (isomorphic to their iterate powers). In recent years, many interesting connections between the above classifications and other dynamical properties have been discovered, especially, when one focuses on more specific families of dynamical systems (subshifts, interval maps, smooth maps on manifolds, actions of particular groups, special flows, non-autonomous systems of certain kinds, etc.). As an example, the relation between entropy and distribution of periodic points has been a frequent subject of study. Additionally, many interesting entropy-like parameters have been invented to study low complexity systems, such as slow entropy, entropy dimension, sequence entropy, etc. Mean dimension, on the other hand, enables one to classify systems with infinite entropy. Some famous conjectures also relate to the above classification, for instance Sarnak’s conjecture or, after Rudolph’s result, Furstenberg’s ×2×3 conjecture (and its generalizations) as well.
In the Special Issue we would like to gather new results in the above spirit: new consequences of positivity or non-positivity of entropy in specific types of dynamical systems, and also the opposite: examples of surprising and counterintuitive coexistence of entropic and non-entropic properties, new tools allowing to classify zero or infinite entropy systems with consequences of such a classification.
Dr. Tomasz Downarowicz
Manuscript Submission Information
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- Zero entropy systems: slow entropy, entropy dimension, sequence entropy, Sarnak’s conjecture, distribution of periodic points, self-similarity
- Positive entropy systems: consequences of positive entropy, chaos, distributional chaos, law of series, distribution of periodic points
- Infinite entropy: mean dimension, distribution of periodic points, self-similarity