Symbolic Dynamics and Its Applications: (Contemporary Mathematics)

This volume contains the proceedings of the conference, Symbolic Dynamics and its Applications, held at Yale University in the summer of 1991 in honor of Roy L. Adler on his sixtieth birthday. The conference focused on symbolic dynamics and its applications to other fields, including ergodic theory, smooth dynamical systems, information theory, automata theory, and statistical mechanics. One hundred thirty-nine participants attended from thirteen countries, representing mathematics, applied mathematics, electrical engineering, and physics departments in universities and in industry. Featuring a range of contributions from some of the leaders in the field, this volume presents an excellent overview of the subject.

Table of Contents:
The torus and the disk by R. L. Adler On the work of Roy Adler in ergodic theory and dynamical systems by B. Weiss The impact of Roy Adler's work on symbolic dynamics and applications to data storage by B. Marcus LR conjugacies of shifts of finite type are uniquely so by J. Ashley A polynomial time algorithm for deciding the forcing relation on cyclic permutations by C. Bernhardt and E. M. Coven Fully positive topological entropy and topological mixing by F. Blanchard The stochastic shift equivalence conjecture is false by M. Boyle Predictions with automata by A. Broglio and P. Liardet Common closing extensions and finitary regular isomorphism for synchronized systems by D. Fiebig Covers for coded systems by D. Fiebig and U.-R. Fiebig $Z$-numbers and $\beta$-transformations by L. Flatto Quasisymmetric conjugacies for some one-dimensional maps inducing expansions by M. V. Jakobson A monotonicity property in one-dimensional dynamics by J.-M. Gambaudo and C. Tresser Finiteness of conjugacy classes of restricted block upper triangular matrices by D. Handelman Polynomials with a positive power being positive by D. Handelman Spectrl radii of primitive integral companion matrices and log concave polynomials by D. Handelman Self-replicating tilings by R. Kenyon Markov subgroups of $({\mathbb Z}/2{\mathbb Z})\{{\mathbb Z}2}$ by B. Kitchens and K. Schmidt On the dimension of some graphs by F. Ledrappier Synchronizing prefix codes and automata and the road coloring problem by D. Perrin and M.-P. Schutzerberger A zero entropy mixing of all orders tiling system by S. Mozes A cocycle equation for shifts by W. Parry In general a degree $2$ map is an automorphism by W. Parry ${\mathbf Z}\n$ versus ${\mathbf Z}$ for systems of finite type by C. Radin Principal vectors of commuting block maps by F. Rhodes On the recurrence of countable topological Markov chains by I. A. Salama Substitutions, adic transformations and beta-expansions by B. Solomyak Finitary isomorphism of $m$-dependent processes by M. Smorodinsky Constant-to-one factor maps and dimension groups by P. Trow Faces of Markov chains and matrices of polynomials by S. Tuncel Classification of subshifts of finite type revisited by J. B. Wagoner Strong shift equivalence of matrices in $GL(2,{\mathbf Z})$ by R. F. Williams.