Glavan V. A.
The structure of linear extensions with the Favard type conditions II. Linear extensions with the additivity property of recurrent motions
Ukr. Mat. Zh. - 1993. - 45, № 4. - pp. 466–471
We study the structure of linear extensions with external powers satisfying the condition of additivity of recurrent motions.
Ukr. Mat. Zh. - 1993. - 45, № 2. - pp. 233–238
The concept of the equicontinuous factor of the linear extension of a minimal transformation group is introduced and investigated. It is shown that a subset of motions, bounded and distal with respect to the extension, forms a maximal equicontinuous subsplitting of the linear extension. As a consequence, any distal linear extension has a nontrivial equicontinuous invariant subsplitting. The linear extensions without exponential dichotomy possess similar subsplittings if the Favard condition is satisfied. The same statement holds for linear extensions with the property of recurrent motions additivity provided that at least one nonzero motion of this sort exists.