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Topological and Symbolic Dynamics
Petr Kůrka, Charles University, Prague, Czech Republic
A publication of the Société Mathématique de France.
Cours Spécialisés--Collection SMF
2003; 315 pp; softcover
Number: 11
ISBN-10: 2-85629-143-0
ISBN-13: 978-2-85629-143-6
List Price: US$79
Member Price: US$63.20
Order Code: COSP/11
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A dynamical system is a continuous self-map of a compact metric space. Topological dynamics studies the iterations of such a map, or equivalently, the trajectories of points of the state space. The basic concepts of topological dynamics are minimality, transitivity, recurrence, shadowing property, stability, equicontinuity, sensitivity, attractors, and topological entropy. Symbolic dynamics studies dynamical systems whose state spaces are zero-dimensional and consist of sequences of symbols. The main classes of symbolic dynamical systems are adding machines, subshifts of finite type, sofic subshifts, Sturmian, substitutive and Toeplitz subshifts, and cellular automata.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and research mathematicians interested in differential equations, geometry, and topology.

Table of Contents

  • Dynamical systems
  • Topological dynamics
  • Symbolic dynamics
  • Minimal symbolic systems
  • Cellular automata
  • Sets, spaces and numbers
  • Main theorems
  • Bibliography
  • Notation
  • Index
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