相关论文: A combinatorial move on the set of Jenkins-Strebel…
Moduli spaces of Abelian and quadratic differentials are stratified by multiplicities of zeroes; connected components of the strata correspond to ergodic components of the Teichmuller geodesic flow. It is known that the strata are not…
The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.
We give an explicit multi-parametric construction for Jenkins-Strebel differentials on real algebraic curves. Roughly speaking, the square of any real holomorphic abelian differential subjected to certain linear restrictions will be a JS…
The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…
Classes of kinetic differential equations are delineated which do have a quadratic first integral, and classes which can not have one. Example reactions corresponding to the obtained kinetic differential equations are shown, and a few…
We describe the connected components of the complement of a natural "diagonal" of real codimension 1 in a stratum of quadratic differentials on CP1. We establish a natural bijection between the set of these connected components and the set…
We consider $n$-dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean displacements these motions correspond to quadrilateral nets…
In this note, we investigate a mixture of combinatorial spectra and stratified simplicial sets, which would be thought of as a model of the spectrum objects of $(\infty, \infty)$-categories.
A celebrated and deep theorem in the theory of Riemann surfaces states the existence and uniqueness of the Jenkins-Strebel differentials on a Riemann surface under some conditions, but the proof is non-constructive and examples are…
This paper is part of a series of three articles with the objective of investigating a stratified version of the homotopy hypothesis in terms of semi-model structures that interact well with classical examples of stratified spaces, such as…
We study the asymptotics of the global fluctuations for the difference between two adjacent levels in the $\beta$--Jacobi corners process (multilevel and general $\beta$ extension of the classical Jacobi ensemble of random matrices). The…
In two fundamental classical papers, Masur and Veech have independently proved that the Teichmueller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore…
This note aims to bring attention to a simple class of discrete dynamical systems exhibiting some complex behaviour. Each of these systems is defined as a self-mapping of the unit square and is obtained by coupling two families of…
In the case of two degree system the pairs of quadratic in momenta Hamiltonians commuting according the standard Poisson bracket are considered. The new many-parametrical families of such pairs are founded. The universal method of…
A contractible simplicial complex is constructed that parametrizes different ways of representing a fixed one-dimensional homology class in a closed orientable surface by isotopy classes of systems of disjoint oriented simple closed curves.…
The paper deals with systems of ordinary differential equations containing in the right-hand side controls which are discontinuous in phase variables. These controls cause the occurrence of sliding modes. If one uses one of the well-known…
We investigate the skew-adjoint extensions of a partial derivative operator acting in the direction of one of the sides a unit square. We investigate the unitary equivalence of such extensions and the spectra of such extensions. It follows…
In this paper we introduce new class of multiplicative interactions of the $\zeta$-oscillating systems generated by a subset of power functions. The main result obtained expresses an analogue of prime decomposition (without the property of…
Here are versions of the proofs of two classic theorems of combinatorial topology. The first is the result that piecewise linearly homeomorphic simplicial complexes are related by stellar moves. This is used in the proof, modelled on that…
We use mathematical induction to prove that the horizontal composition in the class of coherently diagonal complexes is indeed a binary operation. That is to say, the embedding of two coherently diagonal complexes in an alternating planar…