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Using the techniques in topological dynamics, we give a uniform treatment ofLi-Yorke chaos, mean Li-Yorke chaos and distributional chaos for continuousendomorphisms of completely metrizable groups, and characterize three kinds ofchaos (resp. extreme chaos) in term of the existence of correspondingsemi-irregular points (resp. irregular points). We also apply the results tothe chaos theory of continuous linear operators on Fr\'echet spaces, whichimprove some results in the literature.

Chaos for endomorphisms of completely metrizable groups and linear operators on Fr\'echet spaces