The Construction of an automorphism with a continuous spectrum and no square root

Abstract

An automorphism S is called a square root of an automorphism T if S² = T. The Problem of describing the square root of a given automorphism T is completely solvable only when T has a discrete [1], [2] or guasi-discrete spectrum. Katok and Stepin [3] gave a general construction of an automorphism with a continuous spectrum but no square root. In this work, we construct a particular example of this kind of automorphisms using the following result.

Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 1-4