Multidimensional Continued Fractions

This text overview various aspects of multidimensional continued fractions, which in this book are defined through iteration of piecewise fractional linear maps. This includes the algorithms of Jacobi-Perron, Güting, Brun, and Selmer but also includes continued fractions on simplices which are related to interval exchange maps or the Parry-Daniels map. New classes of subtractive algorithms are also included and the metric properties of these algorithms can be investigated by methods of ergodic theory. The recent connection between multiplicative ergodic theory and Diophantine approximation is presented as well as several results on convergence and Perron's approach to periodicity, which has never appeared in book form. Further chapters include the basic properties of continued fractions in the complex plane, connections with Hausdorff dimension and Kusmin theory for multidimensional maps.