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.
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