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Is there a class of measures which is natural for sofic systems in the same way that Markov measures are natural for subshifts of finite type? Motivated by this question, we identify and study a class of finitary measures on sofic systems. We aim to convince the reader that, in addition to answering the above question, those measures are related to Markov measures in the way that sofic systems are related to subshifts of finite type.

Nearly one hundred years ago Jacques Hadamard used infinite sequences of symbols to analyze the distribution of geodesics on certain surfaces. That was the beginning of symbolic dynamics. In the 1930's and 40's Arnold Hedlund and Marston Morse again used infinite sequences to investigate geodesics on surfaces of negative curvature. They coined the term symbolic dynamics and began to study sequence spaces with the shift transformation as dynamical systems. In the 1940's Claude Shannon used sequence spaces to describe infor mation channels. Since that time symbolic dynamics has been used in ergodic theory, topological dynamics, hyperbolic dynamics, information theory and complex dynamics. Symbolic dynamical systems with a finite memory are stud ied in this book. They are the topological Markov shifts. Each can be defined by transition rules and the rules can be summarized by a transition matrix. The study naturally divides into two parts. The first part is about topological Markov shifts where the alphabet is finite. The second part is concerned with topological Markov shifts whose alphabet is count ably infinite. The techniques used in the two cases are quite different. When the alphabet is finite most of the methods are combinatorial or algebraic. When the alphabet is infinite the methods are much more analytic. This book grew from notes for a graduate course taught at Wesleyan Uni versity in the fall of 1994 and is intended as a graduate text and as a reference book for mathematicians working in related fields.

Abstract: "We present some results and conjectures around the following theme: Chebyshev polynomials solve minimax questions about higher derivatives of maps with certain topological entropies or other specifications."

Told in an achingly beautiful voice, Salleys Kitchen conveys the story of a tender first love among brutal racial hatred. Set among the sandhills of a western South Carolina cotton farm it is ripped from the actual events that occurred in that region during the late 1960s. With painstaking realism, the story paints an intense portrait of life as a black person during the Jim Crow Era in the South. Seen through the eyes of a young white boy, lovingly raised since an infant in the southern black culture, his unique point of view articulates his struggle to enter adulthood as a white, black person.