Annals of Combinatorics 1 (1997) 99-104Problems in Combinatorics on Words Originating from Discrete Dynamical Systems James D. Louck Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Received December 18, 1996 AMS Subject Classification: 05A05, 58F08 Abstract. Properties of a family of quadratic maps of the real line are reviewed to illustrate the role of words on two letters in labeling the inverse graph of the nth iterate. Two problems in the abstract theory of words on two letters are described, the solutions of which are essential for the description of the inverse graphs. Keywords: iterated maps, labeling of inverse graph, α-sequences, combinatorics on words References 1. R.L. Bivins, J.D. Louck, N. Metropolis, and M.L. Stein, Classification of all cycles of the parabolic map, Physics D 51 (1991) 3–27. 2. R.L. Bivins, J.D. Louck, N. Metropolis, and M.L. Stein, Classification of all cycles of the parabolic map: The complete solution, in preparation. 3. K.M. Brucks, Dynamics of one-dimensional maps: Symbols, uniqueness, and dimension, Ph. D. Dissertation, North Texas State University Denton, Texas, USA, 1988. 4. P. Collet and J.-P. Eckmann, Iterated Maps on the Interval as Dynamical Systems, Birkhäuser, Boston, 1980. 5. B.-L. Hao, Chaos, World Scientific, Singapore, 1984. 6. M. Lothaire, Combinatorics on Words, Encyclopedia Math. Appl. 17, G.-C. Rota, Ed., Addison-Wesley, Reading, 1981. 7. J.D. Louck, Conway numbers and iteration theory, Adv. Appl. Math. 18 (1997) 181–215. 8. J.D. Louck and N. Metropolis, Symbolic Dynamics of Trapezoidal Maps, D. Reidel, Dordrecht, 1985. 9. N. Metropolis, M.L. Stein and P.R. Stein, On finite limit sets for transformations of the unit interval, J. Combin. Theory 15 (1971) 24–45. 10. L. Sun and G. Helmberg, Maximal words connected with unimodal maps, Order 4 (1988) 351–380. |