Dynamical Systems

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  • What is a shift of finite type? a sofic shift? give an example of each.
  • Give an example of a subshift which is not sofic.
  • What is the Morse shift? Show it is not sofic.
  • Define the zeta function. State a theorem characterizing zeta functions of shifts of finite type and sofic shifts.
  • Calculate the zeta function for some standard examples.
  • What is (topological) entropy? Explain how to compute the entropy of a subshift. Give a formula for the entropy of a sofic shift. Prove the formula is correct.
  • Sketch Lind's proof that every Perron number is the spectral radius of a primitive non-negative integral matrix.

This page was originally derived from this TeX file.

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