Homogeneous spectrum and mixing transformations (Q656246)

It is known that one of the problems in ergodic theory is the determination of possible spectral invariants for various classes of transformations. The aim of the present paper is to solve the well-known Rokhlin's problem (the existence of transformations with continuous homogeneous finite spectrum of multiplicity \(n>1\), meaning that the multiplicity function is constant almost everywhere with respect to the spectral measure on the circle and takes the value \(n\)) in the class of mixing transformations. In particular, the author managed to find out that, for any positive integer \(n\), there exists a mixing transformation with homogeneous spectrum of multiplicity \(n\).