It took a long time to finish, but that's par for the course on a project like this.

Somebody needs to invent a smell-o-meter for gyms

Fear that you might step on a pongee stick and see your foot swell up like some noxious green balloon, fear that some kid in black p. j.'s whose name you couldn't even fit in your mouth might blow your head off with a Russian rifle, fear that you might draw a Crazy Jake on patrol that might want you to blow up everyone in a village where the Cong had been a week before.

The equivalency arises when we add condition of invariance to Li-Yorke scrambled set. In this note we show that for a continuous graph map properties positive topological entropy; horseshoe; invariant Li-Yorke scrambled set; uniform invariant distributional chaotic scrambled set and distributionaly chaotic pair are mutually equivalent..