Units and periodic Jacobi-Perron algorithms in real algebraic number fields of degree $3$
Leon Bernstein · Transactions of the American Mathematical Society · 1975
It is not known whether or not the Jacobi-Perron Algorithm of a vector in ${R_{n - 1}},n \geqslant 3$, whose components are algebraic irrationals, always becomes periodic. The author enumerates, from his previous papers, a few infinite classes of real algebraic number fields of any degree for which this is the case. Periodic Jacobi-Perron Algorithms are important, because they can be applied,