5 ms·
Period Three Implies Chaos (1975) [pdf]
- Cieplak 8y agoTook 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
- espeed 8y agoHow cool that would have been. Would love to hear about any of the class gems, insight or otherwise. What year did you attend?
- meuk 8y agoFrom 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'.
- selimthegrim 8y agoThere was a good blog post that touched on this recently on Scientific American’s website - https://blogs.scientificamerican.com/roots-of-unity/the-couple-that-studies-the-intermediate-value-theorem-together-stays-together/ https://blogs.scientificamerican.com/roots-of-unity/the-coup...
- matthewmcg 8y agoFor 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=Period+three+implies+chaos+james+gleick&hl=en&sa=X&ved=0ahUKEwimn9zVlt3gAhUOhOAKHUeHBEoQ6AEIMTAC#v=onepage&q=Period%20three%20implies%20chaos%20james%20gleick&f=false https://books.google.com/books?id=de4PAQAAQBAJ&pg=PT94&dq=Pe...
- ligotti 8y agoOne the gateway drugs to mathematics. Thanks for the reminder!