On scaling entropy sequence of dynamical system

TL;DR

This paper investigates the properties of scaling entropy as a metric invariant in dynamical systems, confirming its invariance and computing it for specific cases to deepen understanding of its behavior.

Contribution

It establishes the metric invariance of scaling entropy and provides explicit calculations in particular dynamical systems, advancing theoretical understanding.

Findings

Scaling entropy is confirmed as a metric invariant.

Explicit calculations of scaling entropy are provided for special cases.

The paper clarifies properties and behavior of scaling entropy in dynamical systems.

Abstract

We present a series of statements about scaling entropy, a metric invariant of dynamical systems proposed by A. M. Vershik in the late 90's. We show that it is a metric invariant indeed and calculate it in several special cases.