Sensitivity of Uniformly Convergent Mapping Sequences in Non-Autonomous Discrete Dynamical Systems

Abstract

Let H be a compact metric space. The metric of H is denoted by d. And let (H,f1,∞) be a non-autonomous discrete system where f1,∞={fn}n=1∞ is a mapping sequence. This paper discusses infinite sensitivity, m-sensitivity, and m-cofinitely sensitivity of f1,∞. It is proved that, if fn(n∈N) are feebly open and uniformly converge to f:H→H, fi∘f=f∘fi for any i∈{1,2,…}, and ∑i=1∞D(fi,f)<∞, then (H,f) has the above sensitive property if and only if (H,f1,∞) has the same property where D(·,·) is the supremum metric.