We study chaotic plane sections of some particular family of triply periodic surfaces. The
question about possible behavior of such sections was posed by SP Novikov. We prove …

This survey is devoted to questions connected with the Novikov problem of describing the
geometry of level curves of quasi-periodic functions on the plane with different numbers of …

We analyze the rel leaves of the Arnoux–Yoccoz translation surfaces. We show that for any
genus g\geqslant 3 g⩾ 3, the leaf is dense in the connected component of the stratum H (g …

Статья включает обзор последних результатов, полученных при исследовании задачи
Новикова об описании геометрии линий уровня квазипериодических функций на …

We discuss here the electron dynamics in crystals in rather strong magnetic fields. The most
non-trivial part of this topic is the Novikov problem, namely, the problem of classifying non …

At the beginning of the 80s, H. Masur and W. Veech started the study of generic properties of
interval exchange transformations (IETs) proving that almost every such transformation is …

We consider the Novikov problem, namely, the problem of describing the level lines of
quasiperiodic functions on the plane, for a special class of potentials that have important …

The paper is devoted to the Novikov problem of describing the geometry of level lines of
quasiperiodic functions on the plane. We consider here the most general case, when the …

The paper is devoted to the applications of the theory of dynamical systems to the theory of
transport phenomena in metals in the presence of strong magnetic fields. More precisely, we …

We consider the Lifshitz topological transitions and the corresponding changes in the
galvano-magnetic properties of a metal from the point of view of the general classification of …