Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps.

We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties. Further, we study how the invariant measures depend on the parameters of the system. These results were illustrated by a simple example or a risk management model where interval translation maps appear naturally. [ABSTRACT FROM AUTHOR]