| Abstract: |
| For variational monotone recurrence relations we know from the Aubry-Mather theory the existence and properties of foliation or lamination consisting of Birkhoff solutions. In this talk, we discuss for the general monotone recurrence relations the existence of Birkhoff solutions and implications of non-Birkhoff solutions. In particular, we show that a solution with bounded action implies the existence of a Birkhoff solution and the rotation set contains an interval with end points being the Farey neighbours of $p/q$ provided there is a non-Birkhoff $(p,q)$ periodic solution. |
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