Slow entropy and variational dynamical systems

TL;DR

This paper introduces variational properties for dynamical systems with subexponential complexity, computes slow entropy to distinguish variational from non-variational systems, and applies these concepts to specific examples like subshifts and interval exchange transformations.

Contribution

It defines variational properties for subexponential complexity systems and demonstrates their application through explicit calculations on subshifts and interval exchange transformations.

Findings

Some subshifts are not variational based on slow entropy calculations.

Interval exchange transformations are shown to be variational.

Explicit computation of slow entropy distinguishes variational properties.

Abstract

We define variational properties for dynamical systems with subexponential complexity, and study these properties in certain specific examples. By computing the value of slow entropy directly, we show that some subshifts are not variational, while a class of interval exchange transformations are variational.