相关论文: Open level lines of a superposition of periodic po…
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 applications in the physics of two-dimensional systems.…
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 and, at the same time, can also be considered as a model…
We consider Novikov's problem of describing level lines of quasiperiodic functions on a plane for two-dimensional potentials of dihedral symmetry. It is shown that quasiperiodic potentials of this type can have open level lines only at a…
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…
The present article proposes a review of the most recent results obtained in the study of Novikov's problem on the description of the geometry of the level lines of quasi-periodic functions in the plane. Most of the paper is devoted to the…
The paper is devoted to the questions connected with the investigation of the S.P. Novikov problem of the description of the geometry of level lines of quasiperiodic functions on a plane with different numbers of quasiperiods. We consider…
We consider Novikov problem of the classification of level curves of quasiperiodic functions on the plane and its connection with the conductivity of two-dimensional electron gas in the presence of both orthogonal magnetic field and the…
We study tilings of the plane composed of two repeating tiles of different assigned areas relative to an arbitrary periodic lattice. We classify isoperimetric configurations (i.e., configurations with minimal length of the interfaces) both…
We consider here quasiperiodic potentials on the plane, which can serve as a "transitional link" between ordered (periodic) and chaotic (random) potentials. As can be shown, in almost any family of quasiperiodic potentials depending on a…
In this paper we consider periodic orbits of planar linear Filippov systems with a line of discontinuity. Unlike many publications researching only the maximum number of crossing periodic orbits, we investigate not only the number and…
Most known examples of doubly periodic minimal surfaces in $\mathbb{R}^3$ with parallel ends limit as a foliation of $\mathbb{R}^3$ by horizontal noded planes, with the location of the nodes satisfying a set of balance equations.…
A level orbit of a mechanical Hamiltonian system is a solution of Newton equation that is contained in a level set of the potential energy. In 2003, Mark Levi asked for a characterization of the smooth potential energy functions on the…
We study a 2+2 body problem introduced in a previous paper as the circular double Sitnikov problem. Since the secondary bodies are moving on the same perpendicular line where evolve the primaries, almost every solution is a collision orbit.…
Numerical analysis indicates that there exists an unexpected new ordered chaos for the bounded one-dimensional multibarrier potential. For certain values of the number of barriers, repeated identical forms (periods) of the wavepackets…
The full theoretical analysis of the kinetics of multicomponent nucleation is presented. The relief of the free energy with surface excesses was analyzed, the valleys and ridges were described, their mutual interaction was studied. The new…
Various solutions are displayed and analyzed (both analytically and numerically) of arecently-introduced many-body problem in the plane which includes both integrable and nonintegrable cases (depending on the values of the coupling…
New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of linear superpositions of arbitrary number of exact special solutions $u^{(n)}$, $n=1,...,N$ are constructed via $\bar\partial$-dressing…
This article is a survey of the Novikov problem of the structure of leaves of the foliations induced by a collection of closed 1-forms in a compact manifold $M$. Equivalently, this is to the study of the level sets of multivalued functions…
Quantum escapes of a particle from an end of a one-dimensional finite region to $N$ number of semi-infinite leads are discussed by a scattering theoretical approach. Depending on a potential barrier amplitude at the junction, the…
A model, plane symmetric, 3-D potential, which preserves some features of galactic problems,is used in order to examine the phase space structure through the study of the properties of orbits crossing perpendicularly the plane of symmetry.…