Lyapunov Exponents for Non-classical Multidimensional Continued Fraction Algorithms
نویسنده
چکیده
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.
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