CONVERGENCE OF CONTINUED-FRACTION TYPE ALGORITHMS AND GENERATORS

The concept of convergence of continued fraction type algorithms has b een defined a number of times in the literature. We investigate the re lation between these definitions, and show that they do not always coi ncide. We relate the definitions to the question whether or not the na tural partition of the underlying dynamical system is a generator. It turns out that the 'right' definition of convergence is equivalent to this partition being a generator. The second definition of convergence is shown to be equivalent only under extra conditions on the transfor mation. These extra conditions are typically found to be satisfied whe n the second definition is used in the literature.