Families of periodic Jacobi--Perron algorithms in any dimension with period lengths going to infinity
One of the generalizations of the continued fraction algorithm to higher dimensions is the Jacobi–Perron Algorithm (JPA). C. Levesque and G. Rhin obtained the JPA expansion of two parametrized infinite families of degree 3, each depending on two parameters. These expansions are purely periodic. We generalize these families to parametrized families (depending on three parameters) of fields with any degree higher than 3.