- 95-485 Baladi V., Nogueira A.
- Lyapunov exponents for non-classical multidimensional continued fraction
(145K, AMS TeX + 3 postcript figures (fig1.eps, fig2.eps, fig3.eps))
Nov 19, 95
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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.