An analysis of indeterminate points in discrete integrable system

Abstract

We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour of indeterminate points of some integrable maps. As a result, (1) we determine their indeterminacy, (2) find they are `confined' by the map, and (3) obtain a periodicity condition of the map from indeterminate point. Finally, we propose a new type of entropy using the indeterminacy in conclusion.