Using Farey neighbors in the number theory,this paper studies the complexity of high-dimensional cylinder twist mapping systems.In view of the one-to-one correspondence between solutions of monotone recur-rence relations and orbits of high-dimensional cylinder twist mapping,we explored the complexity of solutions of monotone recurrence relations instead.Suppose that there exists a pair of stable Farey neighbors p/q and p'/q'in the rotation set of monotone recurrence relations.A supersolution and a subsolution which exchange rotation numbers p/q and p'/q'are constructed according to the periodic extension method.It then follows from the An-genent's criterion that the system has positive topological entropy.
维普
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