
Period Three Implies Chaos (1975) [pdf] - espeed
http://yorke.umd.edu/papers/Li-Yorke%20Period%20Three%20Implies%20Chaos.pdf
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Cieplak
Took Dr. Yorke’s undergraduate course on dynamical systems at Maryland. By far
my favorite course ever. Interesting to note that the result discussed in this
paper was independently discovered a few years earlier by Sharkovskii [1].

[1]
[https://en.wikipedia.org/wiki/Sharkovskii's_theorem](https://en.wikipedia.org/wiki/Sharkovskii's_theorem)

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meuk
From the wiki page, I am led to believe that he proved a weaker result, being
that if there are cycles of period three then there are cycles of every period
(which is _not_ the period three implies chaos result).

See the second paragraph in the section 'Generalizations'.

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selimthegrim
There was a good blog post that touched on this recently on Scientific
American’s website - [https://blogs.scientificamerican.com/roots-of-unity/the-
coup...](https://blogs.scientificamerican.com/roots-of-unity/the-couple-that-
studies-the-intermediate-value-theorem-together-stays-together/)

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matthewmcg
For context, James Gleick’s _Chaos_ is a great account of this paper and
related discoveries.

[https://books.google.com/books?id=de4PAQAAQBAJ&pg=PT94&dq=Pe...](https://books.google.com/books?id=de4PAQAAQBAJ&pg=PT94&dq=Period+three+implies+chaos+james+gleick&hl=en&sa=X&ved=0ahUKEwimn9zVlt3gAhUOhOAKHUeHBEoQ6AEIMTAC#v=onepage&q=Period%20three%20implies%20chaos%20james%20gleick&f=false)

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ligotti
One the gateway drugs to mathematics. Thanks for the reminder!

