# Jacob's ladders and some unbounded decomposition of the $\zeta$-oscillating systems on products of other $\zeta$-oscillating systems as an $\zeta$-analogue of the prime decomposition

## TL;DR

This paper introduces a new class of multiplicative interactions among $z-oscillating systems, providing an analogue of prime decomposition without uniqueness, inspired by Nikola Tesla's oscillators.

## Contribution

It presents a novel framework for decomposing $z-oscillating systems into products of other systems, extending the concept of prime decomposition in this context.

## Key findings

- New class of multiplicative interactions introduced
- Analogue of prime decomposition established
- Decomposition lacks uniqueness

## Abstract

In this paper we introduce new class of multiplicative interactions of the $\zeta$-oscillating systems generated by a subset of power functions. The main result obtained expresses an analogue of prime decomposition (without the property of uniqueness). Dedicated to recalling of Nicola Tesla's oscillators