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 …

We introduce a new renormalization procedure on double rotations, which is reminiscent of
the classical Rauzy induction. Using this renormalization we prove that the set of parameters …

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 …

Here are two problems. First, understanding the dynamics of a tiling billiard in a cyclic
quadrilateral periodic tiling. Second, describing the topology of connected components of …

An upper bound on the dimension of the Rauzy gasket arXiv:2110.07264v2 [math.DS] 22
May 2023 Page 1 An upper bound on the dimension of the Rauzy gasket Mark Pollicott ∗ …

We consider the behavior of level lines of two-dimensional potentials, which play an
important role in the physics of``two-layer''systems. Potentials of this type are quasiperiodic …

We construct an Arnoux–Rauzy word for which the set of all differences of two abelianized
factors is equal to Z3. In particular, the imbalance of this word is infinite–and its Rauzy fractal …

AS Skripchenko, “Renormalization in one-dimensional dynamics”, Uspekhi Mat. Nauk, 78:6(474)
(2023), 3–46; Russian Math. Surveys, 78:6 (2023), 983–1021 Russian Mathematical Surveys …

The work examines a special behavior of the magnetic conductivity of metals that arises
when chaotic electron trajectories appear on the Fermi surface. This behavior is due to the …