Integral Value Transformations: A Class of Affine Discrete Dynamical Systems and an Application

TL;DR

This paper introduces Integral Value Transformations (IVTs) and Affine Discrete Dynamical Systems (ADDS), explores a Collatz-like problem within this framework, and designs an optimal distributed parallel environment based on ADDS.

Contribution

It defines IVTs and ADDS, applies them to a Collatz-like problem, and develops an optimal distributed parallel environment for these systems.

Findings

Solved a Collatz-type problem in IVT domain in 2011

Analyzed properties of affine discrete dynamical systems

Designed an optimal distributed parallel environment for ADDS

Abstract

In this paper, the notion of Integral Value Transformations (IVTs), a class of Discrete Dynamical Maps has been introduced. Then notion of Affine Discrete Dynamical System (ADDS) in the light of IVTs is defined and some rudimentary mathematical properties of the system are depicted. Collatz Conjecture is one of the most enigmatic problems in 20th Century. The Conjecture was posed by German Mathematician L. Collatz in 1937. There are much advancement in generalizing and defining analogous conjectures, but even to the date, there is no fruitful result for the advancement for the settlement of the conjecture. We have made an effort to make a Collatz type problem in the domain of IVTs and we have been able to solve the problem in 2011 [1]. Here mainly, we have focused and inquired on Collatz-like ADDS. Finally, we have designed the Optimal Distributed and Parallel Environment (ODPE) in the light of ADDS.