  This 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.
