Baladi V., Nogueira A.
Lyapunov exponents for non-classical multidimensional continued fraction 
algorithms
(145K, AMS TeX + 3 postcript figures (fig1.eps, fig2.eps, fig3.eps))

ABSTRACT.  We introduce a simple geometrical two-dimensional continued
fraction algorithm inspired from dynamical renormalization.
We prove that the algorithm is weakly convergent, and that the associated 
transformation  admits an ergodic absolutely continuous invariant 
probability measure. Following Lagarias, its Lyapunov exponents
are related to the approximation exponents which measure the diophantine 
quality of the continued fraction. The Lyapunov exponents for our algorithm 
and related ones, also  introduced in this article, are studied numerically.