Geodesic
Periodic karyon expansions of algebraic units in multidimensional continued fractions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 84-129
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Periodic expansions of algebraic numbers in multidimensional continued fractions are obtained by using multidimensional backward maps and the differentiation method of induced toric tilings. 
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V. G. Zhuravlev. Periodic karyon expansions of algebraic units in multidimensional continued fractions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 84-129. http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a5/

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