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In this chapter, several basic notations in symbolic dynamical systems such as shift spaces, sliding block codes and topological conjugacy are presented. Vertex shifts, edge shifts and shifts of finite type are introduced. They form a fundamental class of subshifts, called topological Markov shifts. State splitting and state amalgamation of finite directed graphs are explained.

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Topological Markov Shifts

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  • 发表日期：

    2025年

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  • Kengo Matsumoto

摘要

In this chapter, several basic notations in symbolic dynamical systems such as shift spaces, sliding block codes and topological conjugacy are presented. Vertex shifts, edge shifts and shifts of finite type are introduced. They form a fundamental class of subshifts, called topological Markov shifts. State splitting and state amalgamation of finite directed graphs are explained.