Functional Analysis and Its Applications

In the paper, the concrete generators are found for the annihilating ideal of the modular symbols associated with SL(s;ℤ). Using this result, the (co)homology of subgroups of finite index is evaluated for SL(s;ℤ).

In this work we continue the study of historically the first version of dynamical entropy. This version was suggested in master’s thesis by D. Arov and went practically unnoticed. The main result of the paper is that the Arov entropy, like the Kolmogorov–Sinai entropy, has the affine property. This, in particular, allows constructing a variety of dynamical systems where the Arov entropy is not determined by the Kolmogorov–Sinai entropy.