# Functional Analysis behind a Family of Multidimensional Continued Fractions:: Triangle Partition Maps

@article{Amburg2017FunctionalAB, title={Functional Analysis behind a Family of Multidimensional Continued Fractions:: Triangle Partition Maps}, author={Ilya Amburg and Thomas Garrity}, journal={arXiv: Dynamical Systems}, year={2017} }

Triangle partition maps form a family that includes many, if not most, well-known multidimensional continued fraction algorithms. This paper begins the exploration of the functional analysis behind the transfer operator of each of these maps. We show that triangle partition maps give rise to two classes of transfer operators and present theorems regarding the origin of these classes; we also present related theorems on the form of transfer operators arising from compositions of triangle…

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