Continued Fractions and Generalizations with Many Limits: A Survey

Abstract

There are infinite processes (matrix products, continued fractions, $(r,s)$-matrix continued fractions, recurrence sequences) which, under certain circumstances, do not converge but instead diverge in a very predictable way. We give a survey of results in this area, focusing on recent results of the authors.

20 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:0709.1909, arXiv:math/0403027