For continuous self-maps of compact metric spaces, we consider the notions generic and dense chaos introduced by Lasota Snoha, their variations for distributional chaos, under assumption shadowing. We give some equivalent properties to uniform (distributional) in terms chains prove equivalence Several examples illustrating main results are also given.

The aim of the paper is to correct and improve some results concerning distributional chaos of type 3. We show that in a general compact metric space, distributional chaos of type 3, denoted DC3, even when assuming the existence of an uncountable scrambled set, is a very weak form of chaos. In particular, (i) the chaos can be unstable (it can be destroyed by conjugacy), and (ii) such an unstabl...