On Shadowing System Generated by a Uniformly Convergent Mappings Sequence.

The shadowing property relationship between a uniformly convergent mapping sequence (f n) n = 1 ∞ and its limit mapping f in non-autonomous systems is discussed. Some sufficient and necessary conditions are given for that (f n) n = 1 ∞ is limit shadowing property, d ̲ -shadowing property or pseudo-orbit shadowing property. In particular, a computer simulation of an example is given to illustrate the shadowing property of (f n) n = 1 ∞ . In addition, it is proved that the sensitivity of (f n) n = 1 ∞ is equivalent to the sensitivity of f under the shadowing system. [ABSTRACT FROM AUTHOR]