Geodesic
Karyon expansions of Pisot numbers in multidimensional continued fractions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 168-195

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Best simultaneously diophantine a pproximations are obtained for Pisot numbers. For this purpose the karyon approximation method is used. Littlewood–Pisot numbers are investigated in detail. 
@article{ZNSL_2016_449_a7,
     author = {V. G. Zhuravlev},
     title = {Karyon expansions of {Pisot} numbers in multidimensional continued fractions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {168--195},
     publisher = {mathdoc},
     volume = {449},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a7/}
}
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V. G. Zhuravlev. Karyon expansions of Pisot numbers in multidimensional continued fractions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 32, Tome 449 (2016), pp. 168-195. http://geodesic.mathdoc.fr/item/ZNSL_2016_449_a7/