On Jacobi-Perron algorithm (Q1805020)

The author considers the Jacobi-Perron algorithm in connection with the transformation \(T\) of \((0,1) \times (0,1)\) into itself. A pair \((a,b)\in (0,1) \times (0,1)\) is called periodic if \(T^ m (a,b)= T^{m+p} (a,b)\), \(p\geq 1\). The main result of the paper expresses a sufficient condition for \((a,b)\) to be periodic in terms of a convergent sequence approaching \((a,b)\).