Dynamical systems and ergodic theory Symbolic dynamics Concept
Shift space
Summary
A shift space, or subshift, is a closed set of infinite sequences over a finite alphabet that is invariant under the shift by one place. Equivalently, it is the set of all sequences that avoid a given list of forbidden finite words. Shift spaces with the shift map are the objects of symbolic dynamics, and they serve as models for coding more general dynamical systems. The full shift, the subshifts of finite type and the sofic shifts are the main classes.
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| Tag | A1XE59ZHNM |
|---|---|
| URI | m2://A1XE59ZHNM |
| Kind | concept |
| Writing | W0 stub |
| MSC | 37B10 |
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Used by
- Cellular automaton
- Expansive homeomorphism
- Symbolic dynamics
- Topological entropy
- Subshift of finite type
- Gibbs measure
- Curtis–Hedlund–Lyndon theorem