| Date: | Wednesday, November 18, 2009 |
| Speaker: | Prof. Ethan Coven
Department of Mathematics Wesleyan University Email: ecoven at wesleyan dot edu |
| Title: | The origins of modern symbolic dynamics |
| Abstract: |
For the purposes of this talk, symbolic dynamics is the study of the iterates, under composition, of the shift transformation on compact spaces of sequences with entries from a finite alphabet.
It is generally believed that symbolic dynamics as defined above started with the seminal papers of Morse and Hedlund (Symbolic Dynamics and Symbolic Dynamics II, Amer. J. Math., 1938 and 1940). However, these papers show very little in common with present-day symbolic dynamics. On the other hand, Hedlund's 1944 Amer. J. Math. paper, Sturmian Minimal Sets, could have been written yesterday. I will trace the change to a 1941 letter from Hedlund to Morse. Much of what I will say, including the Hedlund to Morse letter, appears in Coven and Nitecki, On the genesis of symbolic dynamics as we know it, Colloq. Math. 110 (2008), 227-242. |