We show that the principal algebraic actions of countably infinite groups associated to lopsided elements in the integral group ring satisfying some orderability condition are Bernoulli.
In this paper, we consider measure-theoretical restricted sensitivity and topological restricted sensitivities by restricting the first sensitive time. For a given topological dynamical system, we define measure-theoretical restricted asymptotic rate
with respect to sensitivity, and obtain that it equal to the reciprocal of the Brin-Katok local entropy for almost every point. For topological version we have similar definitions and conclusions.
Let $mathcal{M}(X)$ be the space of Borel probability measures on a compact metric space $X$ endowed with the weak$^ast$-topology. In this paper, we prove that if the topological entropy of a nonautonomous dynamical system $(X,{f_n}_{n=1}^{+infty})$
vanishes, then so does that of its induced system $(mathcal{M}(X),{f_n}_{n=1}^{+infty})$; moreover, once the topological entropy of $(X,{f_n}_{n=1}^{+infty})$ is positive, that of its induced system $(mathcal{M}(X),{f_n}_{n=1}^{+infty})$ jumps to infinity. In contrast to Bowens inequality, we construct a nonautonomous dynamical system whose topological entropy is not preserved under a finite-to-one extension.
