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October 13, 2025Open Access

On the subsystems of certain sofic shifts

Key Points

The theorem confirms conditions for embeddings based on periodic points, extending known results.
Embedding conditions apply between subshifts of different topological entropies, enhancing existing theories.
Krieger's theorem for Markov chains provides a foundational basis for this extension.
This research contributes to understanding the structure of sofic shifts and their substructures.

Abstract

For an aperiodic subshift of finite type Y and for a subshift X with topological entropy less than the topological entropy of Y, a theorem is proved in Krieger: On the subsystems of topological Markov chains, Ergodic Theory \& dynamical systems 1982 2, 195-202, that says that the necessary condition on the periodic points of X and Y for the existence of an embedding of X into Y is also sufficient for the existence of an embedding of X into Y. In this note we point out that this theorem extends to certain classes of sofic shifts as target shifts.

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Cite This Study

Wolfgang Krieger (Thu,) studied this question.

synapsesocial.com/papers/68ece2abd1bb2827d1297510 https://doi.org/https://doi.org/10.48550/arxiv.2507.02717

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