2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62595This paper consists of variations upon the theme of limiting modular symbols. Topics covered are: an expression of limiting modular symbols as Birkhoff averages on level sets of the Lyapunov exponent of the shift of the continued fraction, a vanishing theorem depending on the spectral properties of a generalized Gauss-Kuzmin operator, the construction of certain non-trivial homology classes associated to non-closed geodesics on modular curves, certain Selberg zeta functions and C^* algebras related to shift invariant sets.25 pages LaTeXNumber TheoryDynamical Systems37D35 11M36 10D15 46L89text