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.
The backward continued fraction map and geodesic flow.Ergodic Theory and Dynamical Systems , 4(4):487–492, 1984
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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.