Rational approximations, multidimensional continued fractions, and lattice reduction (Q6611636)

This is a very nice paper on algorithmic and approximation properties of various multidimensional continued fractions. In particular the authors show two main strategies for producing rational approximations in an effective way. They begin with the classical dynamical unimodular continued fraction algorithms and further continue with the algorithms based on the lattice reduction algorithms and homogeneous dynamics. In the last sections the authors deal with the nearest integer Jacobi-Perron algorithm; they describe its associated Markov partition and provide a strategy for proving the existence of an absolutely continuous invariant measure.\N\NFor the entire collection see [Zbl 1542.11001].