Signs of convergence of periodic branched chain shapes of a special form

Abstract

The circle (multidimensional generalization of Worpitsky's Theorem) and the oval regions of the convergence were investigated for $\overrightarrow{p}$-periodic branched continued fractions of the special form. For 1-periodic these fractions the convergence was proved, the truncation error bounds was researched in the angle regions; the necessary condition was established.