Dynamical systems with an even-mulriplicity Lebesgue component in the spectrum

A general construction of ergodic transformations with Lebesgue component of finite multiplicity is proposed. All known examples with this property can be encompassed within the proposed construction. The spectral and combinatorial properties of the transformations are studied. It is shown that the construction permits one to obtain a continuum of spectrally nonisomorphic transformations with even-multiplicity Lebesgue component. As a rule, the transformations have a continuous spectrum. It is proved that continuum many metrically nonisomorphic transformations having the same spectrum are contained in the proposed class. Proof of all the results uses a combinatorial and approximation technique.
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Bibliography: 15 titles.