# An analysis of indeterminate points in discrete integrable system

## TL;DR

This paper studies indeterminate points in discrete integrable systems, developing a method to analyze their behavior, revealing their confinement, periodicity, and proposing a new entropy measure based on indeterminacy.

## Contribution

It introduces a novel method for analyzing indeterminate points in integrable maps and links their properties to system entropy.

## Key findings

- Indeterminate points are confined by the map.
- They exhibit periodicity conditions.
- A new entropy measure based on indeterminacy is proposed.

## Abstract

We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour of indeterminate points of some integrable maps. As a result, (1) we determine their indeterminacy, (2) find they are `confined' by the map, and (3) obtain a periodicity condition of the map from indeterminate point. Finally, we propose a new type of entropy using the indeterminacy in conclusion.