Advances in Mathematical Physics (Jan 2022)
Three Types of Distributional Chaos for a Sequence of Uniformly Convergent Continuous Maps
Abstract
Let hss=1∞ be a sequence of continuous maps on a compact metric space W which converges uniformly to a continuous map h on W. In this paper, some equivalence conditions or necessary conditions for the limit map h to be distributional chaotic are obtained (where distributional chaoticity includes distributional chaotic in a sequence, distributional chaos of type 1 (DC1), distributional chaos of type 2 (DC2), and distributional chaos of type 3 (DC3)).