We investigate a shadowing property which appears naturally in the study of piecewise monotonic maps of the interval. It turns out to be a weak form of the rank one property, a well-known notion in abstract ergodic theory. We show that this new property is implied by finite or even local rank, but that it is logically independent of loose Bernoulliness. We give (counter)examples, including L.B....

In this article, we present a measurable version of the spectral decomposition theorem for Z2-action on compact metric space. process, obtain some relationships with shadowing property and k-type weak extending property. Then, introduce definition measure expanding by using properties Borel measure. We also prove one that occurs whenever is invariantly expanding. All supporting results are nece...

We obtain sufficient conditions for commutative non-autonomous systems on certain metric spaces (not necessarily compact) to be topologically stable. In particular, we prove that: (i) Every mean equicontinuous, expansive system with strong average shadowing property is (ii) recurrently eventual (iii)

The article deals with the essence of national economy de-shadowing concept, as well foreign experience in combating shadow sector. In particular, methods counteracting shadowing such countries USA, Great Britain, France, Poland, Germany, Austria, etc. are summarized. Among most common and effective tools studied countries, following identified: property liability for committing an economic cri...

In this paper, we introduce a Lorentzian Anosov family (LAfamily) up to sequence of distributions null vectors. We prove for each p Mi, where Mi is manifold i Z the tangent space at has unique splitting and varies continuously on via distance function created by torsion-free semi-Riemannian connection. present three examples LA-families. Also, define shadowing property type I II some results re...