Constructing an automorphism with discrete spectrum

Abstract

This work is a desire to construct an automorphism with discrete spectrum using a numerical example. We briefly discuss how some of the definitions and theorems about its behaviour can be implemented and verified numerically. While it is not intended as a complete introduction to measure theory, only the definitions relevant to the discussion in this work are included. It went further to show that a necessary and sufficient condition for a measure-preserving transformation c on a unit circle S\' to be invertible is that it must both be one-one and onto and concludes that it is an automorphism if the real number, α , is one.

JONAMP Vol. 11 2007: pp. 491-496