Li and Yorke established the fact that period 3 implies chaos, which implies that if we have a period 3 orbit in a system then we have a chaotic system. I have seen that in bifurcation diagrams there exists a period 3 window and that an attractor crisis occurs after the period 3 window due to the unstable orbit created by the saddle node bifurcation colliding with the attractor, but am struggling to understand why the period 3 exists, and how it is produced. If anyone could help me that would be great!
2026-03-25 20:34:48.1774470888
Period 3 window in chaos
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Since I cannot comment, hence I am posting this in the answers. Kindly have a look at the Sharkovsky ordering to better understand the origins of the statement period three implies chaos. http://www.scholarpedia.org/article/Sharkovsky_ordering