We will extend the topological Gromov-Hausdorff stability [ 2 ] from homeomorphisms to finitely generated actions. prove that if an action is expansive and has shadowing property, then it topologically GH-stable. From this we derive examples of GH-stable actions discrete Heisenberg group on tori. Finally, GH-stability invariant under isometric conjugacy.

We prove that oriented and standard shadowing properties are equivalent for topological flows on closed surfaces with the nonwandering sets consisting of a finite number critical elements (i.e., singularities or orbits). Moreover, we each isolated singularity flow surface property is either asymptotically stable, backward admits neighborhood which splits into two four hyperbolic sectors.

Pronunciation is essential to appropriate communication because the incorrect use ofpronunciation inevitably leads to the message being misunderstood by the receptor. In spite of itsimportance, L2 learners often regard pronunciation as the most difficult language skill to learn.In this study, shadowing as an act or task in pronunciation, in which the learner tracks the targetspeech and repeats ...

An important property of high altitude platform station (HAPS) Universal Mobile Telecommunications Systems (UMTS) is that unlike terrestrial tower based systems. interference is dependent on the antenna characteristics of HAPS rather than the terrain features (i.e., shadowing) in the service area. In this paper. we exploit this unique HAPS property to propose simple and effective adaptive softe...

— We give a survey of the entropy theory of interval maps as it can be analyzed using ergodic theory, especially measures of maximum entropy and periodic points. The main tools are (i) a suitable version of Hofbauer’s Markov diagram, (ii) the shadowing property and the implied entropy bound and weak rank one property, (iii) strongly positively recurrent countable state Markov shifts. Proofs are...

We study the properties of $ \Phi $-irregular sets (sets points for which Birkhoff average diverges) in dynamical systems with shadowing property. estimate topological entropy set terms on chain recurrent classes and prove that full are typical. also consider $-level whose is a specified interval), relating they carry some ergodic measures. Finally, we problem large deviations considering level...

Firstly, it is introduced that the concepts of G-almost periodic point and G-sequence shadowing property. Then, we discuss dynamical relationship between sequence map {gk}∞k=1 limit g under G-strongly uniform convergence topological group action. We can get (1) Let be converge to where equicontinuous {yk}∞k=1 {gk}∞k=1. If limk → ∞ yk = y, then y an g; (2) are equicontinuous, limsup APG(gk) ⊂ AP...