ﻻ يوجد ملخص باللغة العربية
We establish connections between several properties of topological dynamical systems, such as: - every point is generic for an ergodic measure, - the map sending points to the measures they generate is continuous, - the system splits into uniquely (alternatively, strictly) ergodic subsystems, - the map sending ergodic measures to their topological supports is continuous, - the Cesaro means of every continuous function converge uniformly.
We discuss an invertible version of Furstenbergs `Ergodic CP Shift Systems. We show that the explicit regularity of these dynamical systems with respect to magnification of measures, implies certain regularity with respect to translation of measures;
For every $rinmathbb{N}_{geq 2}cup{infty}$, we show that the space of ergodic measures is path connected for $C^r$-generic Lorenz attractors while it is not connected for $C^r$-dense Lorenz attractors. Various properties of the ergodic measure space
Recently, the dynamical and spectral properties of square-free integers, visible lattice points and various generalisations have received increased attention. One reason is the connection of one-dimensional examples such as $mathscr B$-free numbers w
In this paper it is proved that if a minimal system has the property that its sequence entropy is uniformly bounded for all sequences, then it has only finitely many ergodic measures and is an almost finite to one extension of its maximal equicontinu
Let ${T^t}$ be a smooth flow with positive speed and positive topological entropy on a compact smooth three dimensional manifold, and let $mu$ be an ergodic measure of maximal entropy. We show that either ${T^t}$ is Bernoulli, or ${T^t}$ is isomorphi