Related papers: Inverse Jacobi multiplier as a link between conser…
It's well known that Noether symmetries lead to the conservation laws. Conserved quantities are constructed out of generator of the symmetry - invariant Hamiltonian vector field. Considering more general class of vector fields -…
Jacobi brackets (a generalization of standard Poisson brackets in which Leibniz's rule is replaced by a weaker condition) are extended to brackets involving an arbitrary (even) number of functions. This new structure includes, as a…
We define and study refined Gopakumar-Vafa invariants of contractible curves in complex algebraic 3-folds, alongside the cohomological Donaldson--Thomas theory of finite-dimensional Jacobi algebras. These Gopakumar-Vafa invariants can be…
We consider the complex moment problem, that is the problem of constructing a positive Borel measure on $\mathbb{C}$ from a given set of moments. We relate this problem to the dynamic inverse problem for the discrete system associated with…
The closed string model in the background gravity field is considered as a bi-Hamiltonian system in assumption that string model is the integrable model for particular kind of the background fields. The dual nonlocal Poisson brackets(PB),…
Two-dimensional Hamiltonian systems admitting second invariants which are quartic in the momenta are investigated using the Jacobi geometrization of the dynamics. This approach allows for a unified treatment of invariants at both arbitrary…
We construct (modified) scattering operators for the Vlasov-Poisson system in three dimensions, mapping small asymptotic dynamics as $t\to -\infty$ to asymptotic dynamics as $t\to +\infty$. The main novelty is the construction of modified…
The multi-indexed Jacobi polynomials are the main part of the eigenfunctions of exactly solvable quantum mechanical systems obtained by certain deformations of the P\"oschl-Teller potential (Odake-Sasaki). By fine-tuning the parameter(s) of…
The theory of differential forms began with a discovery of Poincare who found conservation laws of a new type for Hamiltonian systems - The Integral Invariants. Even in the absence of non-trivial integrals of motion, there exist invariant…
We study a system of stochastically forced infinite-dimensional coupled harmonic oscillators. Although this system formally conserves energy and is not explicitly dissipative, we show that it has a nontrivial invariant probability measure.…
We consider the Vlasov-Maxwell equations with one spatial direction and two momenta, one in the longitudinal direction and one in the transverse direction. By solving the Jacobi identity, we derive reduced Hamiltonian fluid models for the…
In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of…
We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein-Stieltjes string. We offer three methods of recovering unknown parameters:…
In this work we discuss the natural appearance of the Generalized Brackets in systems with non-involutive (equivalent to second class) constraints in the Hamilton-Jacobi formalism. We show how a consistent geometric interpretation of the…
The existing paradox between theory and computational experiment for weak solutions of systems of conservation laws in higher space dimensions is arguably resolved. Apparently successful computations are identified with underlying…
Methods based on "(Jacobian) matrix measure" to show the convergence of a dynamical system to a limit cycle (LC), generally assume that the measure is negative everywhere on the LC. We relax this assumption by assuming that the matrix…
Consider the quasi-commutative approximation to a noncommutative geometry. It is shown that there is a natural map from the resulting Poisson structure to the Riemann curvature of a metric. This map is applied to the study of high-frequency…
The standard formulation of Jacobi manifolds in terms of differential operators on line bundles, although effective at capturing most of the relevant geometric features, lacks a clear algebraic interpretation similar to how Poisson algebras…
We develop a geometric framework for the exact integration of Hamiltonian systems based on triangular closure relations among a finite family of functions. Unlike Liouville-Arnold integrability and its noncommutative generalizations, the…
We introduce a maximal operator for the natural analogue of the disc multiplier in the framework of Jacobi analysis and determine the mapping properties of said maximal operator, including weak type endpoint results. In particular we obtain…