Every finitely generated Fuchsian group of the first kind with at least one cusp admits a boundary map whose two-dimensional natural extension has a finite rectangular global attractor, confirming Zagier's conjecture.
Markov maps associated with Fuchsian groups
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Reduction theory for Fuchsian groups with cusps
Every finitely generated Fuchsian group of the first kind with at least one cusp admits a boundary map whose two-dimensional natural extension has a finite rectangular global attractor, confirming Zagier's conjecture.