Dynamical systems defined on a set of idempotent measures

This dissertation investigates quadratic operators that map the n-dimensional simplex of idempotent measures to itself. We introduce the concept of Volterra quadratic operator on the simplex of idempotent measures and provide some general properties of such operators.
A special Volterra quadratic operator is considered and a comprehensive analysis of the dynamical system generated by this operator is given. Moreover, the dynamical systems generated by general Volterra operators defined on 2,3 and 4-dimensional simplices of idempotent measures are studied. For each case, we find fixed points and limits of trajectories.