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During the summer, I did an REU where we focused primarily on one-dimensional dynamics and more specifically kneading theory. One thing that I was always confused about is why the Schwarzian derivatives always seem to pop up in discussions of iterated dynamics on the real line. I understand what a Schwarzian derivative is, but I don't see any intuitive reason that it should show up in this area.

I was wondering if anyone could explain or provide me with a reference that makes the appearance of Schwarzian derivatives in one-dimensional dynamics on the real line seem natural.

Another question I have, is there an intuitive motivation for the Schwarzian derivative itself?

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    you maybe interested in this thread http://mathoverflow.net/questions/38105/is-there-an-underlying-explanation-for-the-magical-powers-of-the-schwarzian-deriv2010-10-17
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    Thanks for the link! Thurston's answer went a bit over my head, but I hadn't realized Sergei Tabachnikov wrote significantly on the topic. I'm taking a seminar class with him at the moment, so I'll probably just try to get him to discuss it.2010-10-17
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    Ha, what a coincidence! Talk about being at the right place. :-)2010-10-17
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    It kind of makes sense now given the subject of all our REU projects. I'll see if I can get him to talk about the topic and if he obliges, I'll tex up some notes and post them.2010-10-17

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