By introducing for monotone recurrence relations pseudo solutions, which are analogues of pseudo orbits of dynamical systems, we show that for general monotone recurrence relations the rotation set is closed, and each element in the rotation set is realized by a Birkhoff orbit. Moreover, if there is an orbit without rotation number, then the system has positive topological entropy, and we can construct orbits shadowing different rotation numbers.

中文翻译：

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单调递推关系的伪解、旋转集和阴影旋转

通过引入类似于动力系统伪轨道的单调递推关系伪解，我们表明对于一般单调递推关系，旋转集是封闭的，并且旋转集中的每个元素都由伯克霍夫轨道实现。此外，如果存在没有自转数的轨道，则该系统具有正拓扑熵，我们可以构造出不同自转数的轨道。