Limiting structures for sequences of linear fractional transformations

Abstract

We introduce restrained sequences of linear fractional transformations which constitute an extension of the class of continued fractions which are generally convergent. The latter concept was recently introduced by L. Jacobsen. Even for elements of the larger class, a well-defined limiting structure exists (even though such sequences need not converge). Exceptional sequences { w n } \{ {w_n}\} for which { T n ( w n ) } \{ {T_n}({w_n})\} does not have the limiting structure associated with the sequence { T n } \{ {T_n}\} are also studied.