Period Three Theorem
Li and Yorke (1975) proved that any one-dimensional system which exhibits a regular cycle of period three will also display regular cycles of every other length as well as completely chaotic cycles.
See also
Chaos, Map Cycle, Sharkovsky's TheoremExplore with Wolfram|Alpha
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References
Borwein, J. and Bailey, D. Mathematics by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A K Peters, p. 79, 2003.Li, T. Y. and Yorke, J. A. "Period Three Implies Chaos." Amer. Math. Monthly 82, 985-992, 1975.Referenced on Wolfram|Alpha
Period Three TheoremCite this as:
Weisstein, Eric W. "Period Three Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PeriodThreeTheorem.html