Shadowing is a method of backward error analysis that plays a important role in hyperbolic dynamics. In this paper, the shadowing by containment framework is revisited, including a new shadowing theorem. This new theorem has several advantages with respect to existing shadowing theorems: It does not require injectivity or differentiability, and its hypothesis can be easily verified using interv...

Most ad hoc and sensor network research assumes idealised radio propagation models without considering fading and shadowing effects. Experimental results have shown that many well-designed protocols will fail simply because of fading and shadowing experienced in a realistic wireless environment. While fading and shadowing for radio propagation are well understood in the wireless communication c...

We study the concepts of continuous shadowing and continuous inverse shadowing with respect to various classes of admissible pseudo orbits, and characterize hyperbolicity and structural stability using the notion of continuous inverse shadowing.

We introduce a notion of shadowing property for actions of finitely generated groups and study its basic properties. We formulate and prove a shadowing lemma for actions of nilpotent groups. We construct an example of a faithful linear action of a solvable Baumslag-Solitar group and show that the shadowing property depends on quantitative characteristics of hyperbolicity. Finally we show that a...

A method of deductive learning is proposed to con trol deductive inference Our goal is to improve prob lem solving time by experience when that experience monotonically adds knowledge to the knowledge base Accumulating and exploiting experience are done by the schemes of knowledge migration and knowledge shadowing Knowledge migration generates speci c migrated rules from general migrating rules...