LYAPUNOV EXPONENTS FOR NONCLASSICAL MULTIDIMENSIONAL CONTINUED-FRACTION ALGORITHMS

We introduce a simple geometrical two-dimensional continued fraction a lgorithm inspired from dynamical renormalization. We prove that the al gorithm is weakly convergent, and that the associated transformation a dmits an ergodic absolutely continuous invariant probability measure. Following Kosygin and Baldwin, its Lyapunov exponents are related to t he approximation exponents which measure the diophantine quality of th e continued fraction. The Lyapunov exponents for our algorithm, and re lated ones also introduced in this article, are studied numerically.