Graphs with pre-assigned Salama entropies and optimal degrees for locally compact Markov shifts
Doris Fiebig · Ergodic Theory and Dynamical Systems · 2003
Suppose that S is a transitive locally compact Markov shift with Gurevic entropy less than log p, where p is an integer. If the inequality is strict, then S admits a graph presentation with degree p. Additionally, we realize any pre-assigned values for the Salama entropies. This result is best possible, since there are examples of Gurevic entropy log p which do not admit a graph presentation with degree p. We also show that every non-compact locally compact Markov shift has presentations without synchronizing blocks.