Dynamical systems with double recursion are undecidable

TL;DR

This paper introduces a specific class of two-dimensional dynamical systems with double recursion and proves that it is impossible to decide whether such systems eventually become zero, highlighting their computational complexity.

Contribution

The paper demonstrates the undecidability of the ultimate zero problem for a new class of two-dimensional dynamical systems with double recursion.

Findings

No decision procedure exists for the ultimate zero problem in these systems.

The systems are shown to be computationally undecidable.

This extends understanding of complexity in dynamical systems.

Abstract

A primitive type of two-dimensional dynamic system is introduced. It is shown that there is no decision procedure able to answer if such a dynamical system is ultimately zero.