TRAJECTORIES OF QUADRATIC OPERATORS WHICH MAP 2 I TO ITSELF

In this paper described some quadratic operators which map the   1  n – dimensional simplex of idempotent measures to itself. Such operators are divided to two classes: the first class contains all n n n   - cubic matrices with nonpositive entries which in each n n dimensional  k th matrix contains exactly one non-zero row and exactly one non-zero column; the second class contains all n n n   - cubic matrices with non-positive entries which has at least one quadratic zero-matrix. These matrices play a role of the stochastic matrices in the case of idempotent measures. For both classes of quadratic maps we find fixed points and their characters. And also, we find trajectories of quadratic maps which map 2 I to itself. In this paper described some quadratic operators which map the   1  n – dimensional simplex of idempotent measures to itself. Such operators are divided to two classes: the first class contains all n n n   - cubic matrices with nonpositive entries which in each n n dimensional  k th matrix contains exactly one non-zero row and exactly one non-zero column; the second class contains all n n n   - cubic matrices with non-positive entries which has at least one quadratic zero-matrix. These matrices play a role of the stochastic matrices in the case of idempotent measures. For both classes of quadratic maps we find fixed points and their characters. And also, we find trajectories of quadratic maps which map 2 I to itself.