Title: On the Novikov problem with a large number of quasiperiods and its generalizations Show Chinese title

Title: 关于具有大量准周期的诺维科夫问题及其推广

Abstract: The paper considers the Novikov problem of describing the geometry of level lines of quasi-periodic functions on the plane. We consider here the most general case, when the number of quasi-periods of a function is not limited. The main subject of investigation is the arising of open level lines or closed level lines of arbitrarily large sizes, which play an important role in many dynamical systems related to the general Novikov problem. As can be shown also, the results obtained for quasiperiodic functions on the plane can be generalized to the multidimensional case. In this case, we are dealing with a generalized Novikov problem, namely, the problem of describing level surfaces of quasiperiodic functions in a space of arbitrary dimension. Like the Novikov problem on the plane, the generalized Novikov problem plays an important role in many systems containing quasiperiodic modulations. Show Chinese abstract

Abstract: 本文考虑了描述平面上准周期函数的等值线几何结构的诺维科夫问题。 我们在这里考虑最一般的情况，即函数的准周期数量不受限制。 研究的主要对象是出现开放的等值线或任意大尺寸的闭合等值线，这些在与一般诺维科夫问题相关的许多动力系统中起着重要作用。 同样可以证明，针对平面上准周期函数得到的结果可以推广到多维情况。 在这种情况下，我们处理的是广义的诺维科夫问题，即描述任意维空间中准周期函数的等值面的问题。 与平面上的诺维科夫问题一样，广义的诺维科夫问题在包含准周期调制的许多系统中起着重要作用。