Aperiodic orbit
= Aperiodic orbit
An <aperiodic orbit> does not repeat with a finite period. An orbit that is not eventually periodic never enters a finite cycle after any number of transients. Aperiodicity alone is insufficient for <chaos>: an irrational circle rotation is aperiodic but has no exponential separation of nearby states. Chaotic interval maps can have both uncountably many <aperiodic orbits> and <dense periodic points>.