One Dimensional p-adic Integral Value Transformations

TL;DR

This paper introduces a new class of p-adic integral value transformations on multi-dimensional non-negative integers, explores their basic structure, and discusses their potential as discrete dynamical systems, opening avenues for further research.

Contribution

It defines the transformations T^(p,k), analyzes their structure for p=1, and introduces the concept of discrete dynamical systems based on IVTs, which is a novel approach.

Findings

Basic structure of T^(p,1) transformations analyzed

Introduced the concept of IVTs as discrete dynamical systems

Highlighted future research directions for IVTs

Abstract

In this paper, a set of transformations T^(p,k) is defined on N_0^K to N_0. Some basic and na\"ive mathematical structure of T^(p,1) are adumbrated and introduced the concept of discrete dynamical systems through IVTs. Latterly, some further research scope of IVTs is highlighted.