Topics in Symbolic Dynamics and Applications

doi:10.1017/CBO9780511758959

This book, first published in 2000, is devoted to developments in symbolic dynamics and comprises eight chapters. The first two are concerned with the study of symbolic sequences of 'low complexity', the following two introduce 'high complexity' systems. Chapter five presents results on asymptotic laws for the random times of occurrence of rare events. Chapter six deals with diophantine problems and combinatorial Ramsey theory. Chapter seven looks at the dynamics of symbolic systems arising from numeration systems, and finally chapter eight gives a complete description of the symbolic dynamics of Lorenz maps.

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Topics in Symbolic Dynamics and Applications

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Contents

Frontmatter
pp i-iv

Contents
pp v-x

FOREWORD
pp xi-xvi

1 - SEQUENCES OF LOW COMPLEXITY: AUTOMATIC AND STURMIAN SEQUENCES
pp 1-34

2 - SUBSTITUTION SUBSHIFTS AND BRATTELI DIAGRAMS
pp 35-56

3 - ALGEBRAIC ASPECTS OF SYMBOLIC DYNAMICS
pp 57-88

4 - DYNAMICS OF ℤd ACTIONS ON MARKOV SUBGROUPS
pp 89-122

5 - ASYMPTOTIC LAWS FOR SYMBOLIC DYNAMICAL SYSTEMS
pp 123-166

6 - ERGODIC THEORY AND DIOPHANTINE PROBLEMS
pp 167-206

7 - NUMBER REPRESENTATION AND FINITE AUTOMATA
pp 207-228

8 - A NOTE ON THE TOPOLOGICAL CLASSIFICATION OF LORENZ MAPS ON THE INTERVAL
pp 229-245

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