Self-duality of multidimensional continued fractions

F. Schweiger introduced the fibred system in [12], to unify and generalize many known continued fraction algorithms.An advantage of a fibred system is that it often provides a systematic construction of an absolutely continuous invariant density.In this paper, we define and study the self-duality of fibred systems, a strong symmetry of a given system.We show that explicit algebraic self-duality holds in many systems and present a curious system with "partial" self-duality.