English

Limiting modular symbols and the Lyapunov spectrum

Number Theory 2007-05-23 v1 Dynamical Systems

Abstract

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.

Keywords

Cite

@article{arxiv.math/0111093,
  title  = {Limiting modular symbols and the Lyapunov spectrum},
  author = {Matilde Marcolli},
  journal= {arXiv preprint arXiv:math/0111093},
  year   = {2007}
}

Comments

25 pages LaTeX

R2 v1 2026-07-22T16:41:28.460Z