This paper investigates the (semi) group action of on, a primary example of non-conformal,
non-linear, and non-strictly contracting action. We establish variational principles of the …

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 …

This paper studies geometric and spectral properties of S-adic shifts and their relation to
continued fraction algorithms. These shifts are symbolic dynamical systems obtained by …

In a recent paper we constructed a family of foliated 2-complexes of thin type whose typical
leaves have two topological ends. Here we present simpler examples of such complexes …

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

We establish an asymptotic formula for the number of integer solutions to the Markoff-
Hurwitz equation x 21+ x 22+...+ x 2 n= ax 1 x 2... xn+ k. When n≥ 4, the previous best result …

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 …

The Rauzy gasket $ R $ is the maximal invariant set of a certain renormalization procedure
for special systems of isometries naturally appearing in the context of Novikov's problem in …