## Dynamics of generalizations of the AGM continued fraction of Ramanujan.

### Russell Luke, Simon Fraser University

We study several generalizations of the AGM continued fraction of Ramanujan inspired by a series of recent articles in which the validity of the AGM relation and the domain of convergence of the continued fraction were determined for certain complex parameters. A study of the AGM continued fraction is equivalent to an analysis of the convergence of certain difference equations and the stability of dynamical systems. Using matrix analytical tools, we determine the convergence properties of deterministic, and stochastic difference equations and their corresponding continued fractions. This is joint work with Jonathan Borwein.