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Mathematical analysis demonstrates that density-equicontinuity inhibits Devaney chaos in discrete dynamical systems, highlighting new criteria for identifying chaotic behavior.
This paper studies density-based equicontinuity in time-varying discrete dynamical systems. It is shown that density-equicontinuity and almost density-equicontinuity are equivalent in minimal systems and both inhibit Devaney chaos. Two chaos criteria are established by combining nondensity-equicontinuity or nonalmost density-equicontinuity with typical chaotic conditions. Further, the equivalence between Banach density-equicontinuity and Banach mean equicontinuity is proved, and the preservation properties of several density-based equicontinuity notions in the finite products setting are verified. These results extend the theory of density-based equicontinuity for time-varying discrete dynamical systems.
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Zhang et al. (2026) studied this question.
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