On zero entropy and quasi-discrete spectrum for automorphisms

Quasi-factors of Zero-entropy Systems

For minimal systems (X, T) of zero topological entropy we demon-strate the sharp difference between the behavior, regarding entropy, of the sys-tems (M(X) , T) and (2x , T) induced by T on the spaces M(X) of prob-ability measures on X and 2x of closed subsets of X. It is shown that thesystem (M(X) , T) has itself zero topological entropy. Two proofs of this the-orem are give...

Scaling entropy and automorphisms with purely point spectrum∗

We study the dynamics of metrics generated by measure-preserving transformations. We consider sequences of average metrics and entropies of the measure with respect to these metrics. The main result, which gives a criterion for checking that the spectrum of a transformation if purely point, is that the scaling sequence for the -entropies with respect to the averages of an admissible metric is b...

On the Discrete Cumulative Residual Entropy

Quantum Dynamical Systems with Quasi–Discrete Spectrum

We study totally ergodic quantum dynamical systems with quasi–discrete spectrum. We investigate the classification problem for such systems in terms of algebraic invariants. The results are noncommutative analogs of (a part of) the theory of Abramov. Supported in part by the National Science Foundation under grant DMS–9801612

On quasi-zero divisor graphs of non-commutative rings

Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for $a,bin R$. The quasi-zero-divisor graph of $R$, denoted by $Gamma^*(R)$ is an undirected graph with all nonzero zero-divisors of $R$ as vertex set and two distinct vertices $x$ and $y$ are adjacent if and only if there exists $0neq rin R setminus (mathrm{ann}(x) cup mathrm{ann}(y))$ such tha...