| Abstract: |
| We discuss the effective uniqueness of entropy-maximizing measure of discrete time geodesic flows on graphs. Namely, if $\\phi$ is a discrete time geodesic flow on a graph and $\\mu$ is a $\\phi$-invariant probability measure with measure-theoretical entropy close to the topological entropy of $\\phi$, then $\\mu$ is close to the unique entropy-maximizing measure of $\\phi$. Analogous results has been obtained for toral automorphisms by Polo, for shift maps on symbolic systems by Kadyrov, and for Cartan actions on $p$-adic groups by Ruhr. |
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